In a quiet little town surrounded by the mountains, Tomoki Sakurai lives a peaceful life with his somewhat Megaton Karate Chop-prone childhood friend waking him up in the morning. That, and the recurring dream of a girl in the sky. At the same time, school eccentric Eishirou Sugata has been witnessing an unidentified thing moving above the Earth, with nobody able to figure it out. Through a series of circumstances, Tomoki ends up being the only one around when the thing falls to Earth near his hometown. In it is a girl in skimpy clothing with angel wings, calling herself an Angeloid. Her name is Ikaros. Things just got a lot more interesting...whether our hero likes it or not.Sora no Otoshimono is a 77-chapter manga created by Suu Mikazuki (who previously wrote Watashi No Messiah Sama) that spawned (currently) two anime seasons and two movie releases. The anime first season was in the fall of 2009, with the second, Sora no Otoshimono forte, at fall 2010. The first movie, The Angeloid of Clockwork, was released June 25, 2011, with the sequel Eternal My Master, released on April 26, 2014.Funimation has licensed the first two seasons of the anime and the movie under the name "Heaven's Lost Property". You can find it here.
This is even lampshaded when she was able to enroll herself into Tomoki's class.
Accidental Pervert: For all Tomoki's intentional pervertedness, walking into Mikako's private hot springs was not something he meant to do. This is one of the few times it's played straight. Most of the time, this trope is averted.
A-Cup Angst: Nymph. It's a bit of a sore point for her.
All-Loving Hero: Tomoki is either a parody of this or a more humane one. While a complete pervert and having many, many flaws both in character and belief; he is the most loving, caring, compassionate being in the entire Verse and ready to put his life on the line for his friends and those in need without a second thought, to the point that nine out of ten CMOA and CMOH are done by him in the series.
Alternate Character Reading: All the episode titles make use of this, with the meanings complementing each other in odd ways. For example, episode eight has "amount of blood spilled" read as "festival".
Alternate Continuity: The TV-and-movie-verse diverges from the manga at episode 11 of forte, and is now a separate continuity.
Amusing Injuries: Tomoki, very often. One notable example, he gets karate chopped so hard by Sohara that she sends him flying into the air and he crashes down a few minutes later into the pavement like a javelin. A naked javelin.
Beach Episode: Set at Mikako's private Deserted Island. Finally subverted; everything was a play of Mikako and her father to punish Tomoki and collect good embarrassment material. Episode six is a more traditional beach episode.
Actually the author has them go to the beach a lot. Most of the time it's just setting up silly gags or tournaments to torture Tomoki. Others are more serious.
Case in point, when Nymph's wings were ripped off, Tomoki looked pissed.
Beehive Barrier: Ikaros' Aegis defense system (a full version of this trope) and Astraea's Aegis-L defense system (more powerful, but only generates from the front.)
Berserk Button: Ikaros goes into the Tranquil Fury kind whenever she thinks her watermelons are in danger. And God help you if you threaten Tomoki.
What are you going to do... to my Master?
As of chapter 51, even Tomoki isn't immune to her rage if her watermelons are in danger.
Beta Couple: Eishiro and Mikako. Though the exact details are sketchy thus far, it's pretty clear these two have a past relationship and deep feelings for each other. Eishiro can frequently been seen protecting or using his body as a shield for Mikako when she's in danger of being hurt when things get serious. Mikako has a special pet name for Eishiro (Ei-kun), and gets crazy mad (more so than usual) when another woman is making moves on him. In the anime, Mikako flat out states that Ei-kun is the only man for her. Of course Mikako being Mikako, she's just as likely to try and kill Eishiro along with everyone else... but she'll probably take greater pleasure because it's him.
BFG: Both Ikaros' Apollon weapon system (a large bow that fires energy arrows) and the Hephaestus, which actually is a BFG seeing how it is an energy cannon capable of vaporizing mountains.
Oregano uses a gatling gun. And a pistol that accompanies the sound effect Boom, Headshot in Chapter 53.
BFS: Astrea's sword gets to stretch SOOOOO big against her fight with Chaos.
Big Damn Heroes: Tomoki, Ikaros, Sugata and Sohara save Nymph from the Harpies.
And later, Tomoki saves Nymph from Astraea when Minos turns them against each other.
Later, Yoshitsune saved Sugata after the world-destroying device activated.
Bitch in Sheep's Clothing: Oregano, the new Angeloid introduced in chapter 52. Putting up a Ikaros-like demeanor as a facade, while bullying Nymph when Tomoki isn't around? Even pulling a Wounded Gazelle Gambit so Nymph becomes the villain in Tomoki's eyes? Of course, Mikako was the one who gave her the ability to speak in the first place ,so...yeah.
Blatant Lies: Ikaros uses this trope once to say the opposite of what she means. She mentions to Sohara that she lost a little weight, and when its clarified later, Sohara is horrified that she gained weight. Ikaros also mentions that Mikako is a very nice person, and when Mikako asks if Ikaros really meant it, the Angeloid this time pulls this trope off beautifully, with Mikako being none the wiser about it.
Book Ends: In the first and last episodes of the first season, Sugata tests one of his hangliders, each time saying quietly to himself, "The wind is picking up. And while I'm not too happy with its direction, it won't affect my takeoff."
Break the Cutie: Chapter 47 is completely devoted to breaking Chaos. She finally realized what love actually is and attempted to go back to Synapse, but the Master blasts her with his strongest weapon. She survives and goes to Tomoki's house but accidentally overhears him say that Angeloids should leave and never come back. She starts crying, and decides that love is pain again. Then she dives to the bottom of the ocean. The entire time, she held on to the shoes Tomoki gave her.
What makes this even worse is that the scene then shifts to Tomoki sitting in the playground where he met Chaos, and he has a bunch of toys all set for her to play with.
And now she not only has all the memories of one of the kindest and most loving cast members all wrapped up in her head, but she just stabbed Tomoki through the friggin' heart. Seems like the author is dedicated to pushing the poor thing until she finally snaps so bad that she has to be put down.
Breaking Speech: Minos pulls this off in Chapter 55 towards Nymph and Daedalus, playing their emotions about how both of them desired Tomoki and Ikaros dying was the best for both of them. Nymph tells him to STFU.
Cerebus Syndrome: While the series always has had a fair bit of moodswings, the later chapters really start to turn dark with the more serious moodswings coming in greater frequencies and major characters starting to drop of like flies.
Chains Of Love: Prominent between Tomoki and Ikaros after their first meeting.
Chekhov's Gun: Sohara's increasing bustline is noted early on then revealed in the last chapter.
The Chew Toy: Tomoki, whenever Mikako comes up with a new scheme for her own personal enjoyment.
Chivalrous Pervert: Tomoki for all his many faults never takes advantage of the fact he has two "girls" that wantto be his slaves and are quite willing to go pretty far to get him to be their master. To his eternal credit he is horrified by the idea and tries to teach them to be independent sentient creatures.
Clothing Damage: Sohara in Episode 4, Tomoki more often. In fact the later chapters take this to Inukami-like levels, with Tomoki reduced to naked chibi Tomoki every time he gets beaten up, flushed down the toilet and so on.
Cloudcuckoolander: Sugata, who boldly eschews thinking in terms of reality in order to prove his theories.
Despite this, he's also the cast's Smart Guy. On his second visit to Synapse, he could already outwit some combat Angeloids with planning that borders on omniscient. Later he manages to gain enough competency with the Angeloids' technology to repair one of their cards.
Comically Missing the Point: In the movie, when Sohara, Nymph, and Astraea confront Tomoki about having a secret relationship with Hiyori, the first two ask him relevant questions regarding the possible relationship. Astraea, on the other hand, is upset that Tomoki gave food to Hiyori, rather than herself.
Companion Cube: Ikaros carries around a watermelon for several episodes until Tomoki tells her that it's probably gone bad by then. A funeral is held for the departed fruit. Though she quickly finds another one. In the manga, this fondness of watermelons leads to her growing an entire patch of them.
In fact, Ikaros has an affinity for anything large and spherical: watermelons, globes, Mikako's father's head. They might represent unhatched eggs to her, as they seem to trigger her nurturing instincts.
Continuity Nod: In forte, Mikako mentions the former Pretty-kuns. They all got lost or died in season 1.
Consummate Liar: Ikaros, after hearing that it's human to lie, ends up saying the opposite of whatever she thinks, which confuses everyone. At the end, she does tell the truth, but Sohara finds the truth not wholly flattering. Ikaros continues her lie to Mikako, because that's really the best option.
Covert Pervert: Sohara. In the manga, she had a dream where she was a very willing participant in Tomoki's cosplay fantasies. If that's not enough, the first episode of the 2nd season depicts this information in all of its glory, removing all doubt about Sohara's own twisted and perverted fantasies. In an episode of the first season, she talked about all the things she would want to do with Tomoki after possibly winning 10 million yen. One of them involved taking Tomoki into an outdoor bath with her, which would have been in an inn she made reservations for.
Also, in the unaired episode (which was released as an OVA), when Tomoki asks Sohara what kind of dream did she have the night before, she apparently dreamt of being at the altar with Tomoki as the groom. Then he leans in for (what many might think) a kiss, but ends up groping her breasts. Apparently, she doesn't mind if Tomoki does perverted things to her.. but only her and after they're married.
Dark Is Not Evil: The Satsukitane family. Sure, they're the local yakuza, their heir Mikako has a devious streak, and they have a habit of chopping off people's heads if they use their private hot spring, but their whole reason for existing is to protect that hot spring from being used by anyone else. That's because if anyone other than the Satsukitane family uses it, Sorami City will be hit by all sorts of natural disasters, such as famines, earthquakes and tornadoes. Other than the rather violent consequences they inflict on trespassers (which is implied to be something they find to be regrettable but necessary), the enforcers and the head of the family itself seem to be fairly affable people.
Daydream Surprise: Mixed with Imagine Spot and All Just a Dream with Tomoki and Astraea imagining they are dogs looking for a good home. Long story short it ends with them licking each other then wondering what they were doing.
Death Is Cheap: Sometimes. Tomoki has been "killed" as a joke before, and the entire population of Earth was wiped out in the second episode, without long-term consequences, but other deaths (the Pretty-Kuns, for example) are permanent.
Despair Event Horizon: Pretty much everyone in Tomoki's Unwanted Harem hits this when Tomoki dies in Chapter 71; especially Chaos, who accidentally killed him when trying to defend herself from an enraged Nymph.
Subverted. Tomoki doesn't die, much to the relief of his harem, except Chaos doesn't know that, since she flew away after accidentally impaling him, so she's still at the Despair Event Horizon.
Disproportionate Retribution: Usually happens with Sohara beating up Tomoki for the most trivial of things, such as when she gets jealous at Tomoki for merely teaching Ikaros how to swim. Or nearly getting beheaded for going into a bathing area. Or having the military called in on him for Ikaros freeing some animals at the zoo (who also seemed to target him as well for some reason). Poor guy just can't catch a break.
I wouldn't call the chop for teaching Ikaros how to swim Disproportionate. If Pretty Girl #1 invites you to a Romantic Weekend for Two and you spend all your time with Pretty Girl #2, you may reasonably expect some blowback.
The Ditz: For all the power Astraea has, she was short-changed in intelligence. Nymph even says that they shouldn't worry when they found out that an Angeloid sent to kill Tomoki was her.
Do Androids Dream?: It's something of a taboo for first generation Angeloids to dream, in part because they don't even sleep. It becomes something of an issue for Nymph when she starts becoming more human.
Sugata eventually explains to her that dreams do not only happen during sleep, but it is also what you desire to happen.
Does Not Know Her Own Strength: All the Angeloids, but specially Ikaros. Really, when her try to be "close" to Tomoi ended burying his face in to the wall by the force of her cheek, you got a problem. Tomoki was not amused.
Double Standard: In the manga, when Tomoki's mom shows up, turns out that she's as big a pervert as he is, but targets both girls and guys. She chases girls around, fondles their breasts, and proposes marriage to guys (her response to asking where her husband is a cheerful "I lost him somewhere"). She gets away with it, though, with the characters simply putting up with it in mild annoyance as opposed to the usual violent retribution Tomoki's actions receive... in fact, Tomoki gets beaten up for stuff his mom does. The very end of the chapter does subvert it somewhat, showing Sohara's Spear Counterpart of Tomoki's father about to smack her, but his mother still takes far less abuse and doesn't get as beat-up-looking as he usually does.
Early-Installment Weirdness: From Chapter 1 to chapter 10 Tomoki was more a generic harem guy, even with a "tragic" backstory, non-chibi form most of the time and while pervert, it was barely his deafening characteristic. It was after Nymph joined the cast and the appearance of the Master that the series got his tragy-comedy mecha battle style, nonsensical Family guy-ish slice of life that made it so loved.
Empty Piles of Clothing: After a satisfying day of having his every wish fulfilled by Ikaros, Tomoki jokes that the only thing left to do is 'take over the world'. The next day, after Ikaros's card decides that no one would accept his rule, the card erases everyone on earth, leaving all their clothes behind.
Even Evil Has Standards: In the movie, after Hiyori joins the New World Discovery club, Tomoki attempts to get her to leave by making her do seemingly humiliating things, such as sniffing panties. Oddly enough, Hiyori does everything he asks without shame or flinching. During the final event, he attempts to make her eat a plate of rice topped with some edible panties, which he apparently does on a regular basis as evidenced by the cook knowing what "his usual" meant. But as she begins, he starts feeling guilty about making her do such a thing. So he swipes the food, and eats it himself.
This is actually shown right off the bat, when Ikaros first shows up. When she tells Tomoki she'll do anything he asks, being a pervert he asks her to strip, which she immediately starts to do. The moment she would actually show anything, he stops her and covers her with his jacket, realizing that it would be wrong to take advantage of her. The fact that he has limits to his perversion basically kicks off the whole plot.
Evolving Credits: The ending changes every episode, and is based on something that happened during that episode.
Expy: The creator seemed to re-use some of his character designs from Watashi No Messiah Sama. Particularly comparable is Tomoki with Shinya (especially from the earlier volumes of Messiah-sama) and Sugata with Shinya's Homeroom Teacher.
Minos, along with some Angeloids, regard humans as little more than bugs.
Also Tomoki, surprisingly. At least, when anyone ships him with an Angeloid, he loudly protests that they have wings fer cryin' out loud! Wings!
Tomoki is less racist and more unwilling to take advantage of the Angeloids' complete willing subservience. Notice his confession to Ikaros during the tournament arc, and his reaction to Ikaros' confession when she burns up to be less "I'm not reciprocating that!" and more "Why the hell are you telling me this now!"
Flexible Tourney Rules: Averted. Ikaros gets disqualified immediately when she uses homing lasers in a wrestling tournament.
For the Evulz: Invoked by the Synapse Master, who seems to enjoy torturing Nymph and causing havoc for the human characters...usually Tomoki.
Mikako also seems to enjoy utilizing this trope on other characters as well...usually Tomoki.
From Bad to Worse: At the end of forte episode 10, Chaos returns to the surface with a brand new look. The latest chapter of the manga instead has Chaos absorbing a Marine Combat Angeloid, directly disobeying an order from her Master thanks to her self evolution program.
Ikaros barely manages to defeatMelan. It looks like it's over for now...then about dozen or so Type Two Nymphs and Astraea show up.
Chaos spends the entirety of a chapter chasing Hiyori around to "eat" her. After Chaos manages to control herself and Hiyori sees how broken she is, she hugs her and it seems things will finally be ok for Chaos...and then Hiyori impales herself on Chaos' wings to make her understand hurting people is wrong, pushing her further down the Despair Event Horizon. Then, after she reveals herself as an angeloid to Tomoki, a hell-bent on revenge Nymph starts attacking Chaos, who never fights back, remembering Hiyori's words. In the end, Tomoki gets impaled by Chaos' wing when he tried to stop the fight, most likely killed, causing Chaos to reach the deepest regions of the Despair Event Horizon. Damn...
Gainaxing: Common, with the most frequent offenders being Ikaros and Astraea.
Gatling Good: Ikaros, during the first summer festival. Also Oregano in Chapter 53.
Gecko Ending: forte completely diverges from the manga starting from episode 11.
Generation Xerox: We meet Tomoki's parents in chapter 49 and find it that Tomoki takes after his MOTHER.
Genre Savvy: Mikako can instantly predict that Tomoki living with Ikaros will lead to hilarious Not What It Looks Like moments in front of Sohara. Even before that, Tomoki knows that bringing Ikaros home is going to dramatically alter his life as he knows it.
Goofy Print Underwear: The impetus for the second episode. An ill-timed Panty Shot of dog-print panties leads to Sohara wearing nothing at all through the latent power of a card. The events of this ultimately lead to panties flying across the world like a flock of very strange birds.
In-universe, Tomoki's porn and stolen panties stash.
Happily Ever After: Perhaps the only happy end to a chapter for Tomoki is in the side chapter where Ikaros destroys his entire Porn Stash due to a misinterpretation, and she decides to make it up to him by gathering all the porn in town for him.
Happiness in Slavery: Ikaros was created to serve her master and sees no problem with it, though Tomoki and the others attempt to break her out of this.
On Nymph's end, however, it's shown that slavery is not at all a happy thing, and the point is driven in when she and Ikaros discuss smiling. Though when she becomes a masterless Angeloid, she laments about not having a master, but is slowly growing out of it and starts expressing desires of her own.
Could still be played straight with Nymph. She actually begged for Tomoki to give her an order while trying to hack a Brainwashed and Crazy Hiyori in chapter 40.
Ikaros is shown to be breaking out of this habit by around chapter 30, by disobeying Chaos!Tomoki's orders to kill Nymph. She proceeds to obey Chaos!Tomoki's orders to destroy herself afterwards, so her progress isn't far, but it's a start.
It seems that the moral of the manga is herding over is that Tomoki must accept that Angeloids are Angeloids and not humans and that they need a Master instead of the freedom he continually spews and accept them for who they are, not what they should be. Also, just because you had power over somebody in someway, doesn't mean you have to be a dick about it.
Hoist By Her Own Petard: When Sohara punishes Tomoki by wishing for any pair of panties that he even so much as looks at to instantly explode, he notices that she wasn't wearing any pants at the time, so he tricks her to stand up and walk away from her bedroom window by saying there's a giant bug on her wall. She realizes her mistake as soon as the panties she was wearing explodes on her.
Idiot Hair: Both Tomoki and Ikaros have one. In Tomoki's case, it's shown all the time while Ikaros' ahoge acts as an antennae that can sense when Tomoki is in danger. Since it wags around, her ahoge is also an example of Expressive Hair.
Ill Girl: Sohara could not go to school before her adolesence due to chronic illness, and hence befriends the boy next door; Tomoki.
Lyrical Dissonance: Mikako's character song, the title of which can be translated as "Princess Kill Them All", is a sweet, poppy tune with Mikako singing about what she wants. Death, destruction and ruling the Earth without mercy.
Informed Flaw: Angeloids supposedly can't smile; although Ikaros does show that trait, Nymph is very obviously smiling on multiple occasions even in the episode where Ikaros and Nymph are discussing this, including flashbacks showing Nymph smiling. The problem seems to be that Nymph has never genuinely smiled, not that she has never physically done the action.
Jerk with a Heart of Gold: While it might be a bit far to call Tomoki a jerk, he definitely does have a nice heart. Even though his perverted antics border on sexual assault at times.
Journey to the Center of the Mind: Forte's first episode is a dream jumping episode. Sohara's dream, in particular, stands out, though everyone's head is far from sane.
The Juggernaut: Chaos is a Moe Token Mini-Moe and is the most resilient Angeloid ever created. Hell, she shrugged a direct attack of the mightiest weapon from Synapses... because she was to busy having an existancial crisis to notice.
Kick the Dog: Minos. The best example of this is when he forces Nymph to crush a small bird she made friends with, solely because it amused him.
Legendary Carp: In the yo-yo breast fishing game Mikako dreamed up, Tomoki puts Sohara into this role. Needless to say, she's not happy with it.
Light Is Not Good: Synapse and its inhabitants, especially the master. All the inhabitants wear togas and have angel-like wings, while the whole of Synapse has some sort of Crystal Spires and Togas air to it, all of which are likely meant to symbolize some sort of divine nature to them. However, their ideas of what is entertaining include mass destruction of the "downers" on the Earth's surface and threatening their "toys'" destruction while hearing them beg for their lives. Can be considered a variation of God Is Evil, since they appear to represent Heaven.
Limited Wardrobe: Sugata. During the Pool Episode, he was asked why he was wearing his uniform, to which he responds that he doesn't have any other clothes.
Love Confession: Hiyori gives one to Tomoki in the movie. Oddly enough, he doesn't seem to reject it, and spends the next scene fretting over it quite a bit.
Nymph later nearly gives him one as well, but its cut short when the Angeloids sense something wrong.
In chapter 53, Tomoki confesses to Ikaros that he likes her before fighting her in the tournament.
Love Dodecahedron: Parodied in the beginning of episode 10, where Mikako draws up a (mostly inaccurate) love chart...that even has her dog on it.
Sugata:Et tu, pooch?
Love Potion: Nymph does a variation of it, by using some technobabble to make Tomoki appear as every girls' ideal man. He decides to show off, but gets a Groin Attack as soon as Nymph decides to remove it.
Mood Whiplash: Most of the chapters are focused on a sort of-Slice of Life harem comedy, but there are pieces of heavy drama that sometimes comes out of left field. A good chunk of which comes from Synapse's master, or for dramatic effect, often corresponding with Cerebus Syndrome.
Mundane Utility: The first thing Tomoki asks for when he gets himself a smoking-hot Angeloid sex slave is...a billion dollars. Doesn't stick due to a Reset Button.
Nice Job Breaking It, Hero: Tomoki says the phrase "Angeloids should not come back" which is not meant to be taken seriously, but ends up causing the literal minded Chaos who has just been blasted by her own master, to undergo a Villainous Breakdown. This breakdown leads her to come to the conclusion that "Love is Pain" and that she should acquire more 'intelligence' by eating others, which indirectly causes Hyori Kazane's death.
When Nymph finds out about Hyori's death (whom she just befriended), she duels Chaos. This leads Chaos to unintentionally killing Tomoki when he throws himself in between them. This causes Chaos's mind to go Villainous BSOD, made all the worse by her newly acquired conscience.
Nice Guy: Seriously, besides his Vouyerism and perverted episodes, Tomoki is the single, nicest being in the entire series and one of the nicest in anime. Its like what you get if you combined Jesus with Howard Stern.
No Kill Like Overkill: During one episode of forte, Nymph and Astraea are hungry, and the only food around is Ikaros' watermelon patch. Nymph notes to Astraea that "Once, a lot of bugs were flying around here. Alpha [Ikaros] blasted them all with her Artemis
Omnicidal Maniac: Minos has been messing with the the cast, making new and more powerful Ageloids and in general acting like a mad man because he wants to destroy "This Stagnant Reality".
Heck, in that chapter he freely admits that being nice or even remotely humane, is just outright too difficult and unreasonable for him. He can only accept a literal killing solution to everything.
Once an Episode: Every episode has a Cold Open with Sugata introducing the audience to a new concept related to the New World, usually working in a bit of history or science with it. Later episodes in the first season subverts his targeted audience towards Mikako, who happened to be present to listen and discuss his lessons with him.
Pretty Freeloaders: Nymph, and Astraea seems to do this as well, visiting Tomoki's house often for the free food.
Rapid-Fire Fisticuffs: Sohara does a Karate-chop version against Tomoki, and Sugata engages in this with the bears that share his mountain home.
Really Gets Around: Tomoki's grandfather (Tomozō Sakurai) claims he slept almost every girl in the world. Now he phrases this as that he only needs to sleep with 2,957,272,615 more woman to sleep with every woman in the world.
Total world population in 2010 was 6.9 billion. If half were women, then he's really only slept with about 493 million. Quite impressive, but not almost every girl. They must blur together after the first hundred million or so.
Real Song Theme Tune: Starting from episode two, every ending theme is an old song repurposed for the episode. The great majority are covers by the SoraOto cast, but one (episode five) is by the original singer (though the live concert has it covered by Sohara and Nymph's seiyuu).
The best part of it? Tomoki uses the bombing panties curse to his advantage; when Sohara explains any pair of panties will explode if he sees them, effectively locking him in his room, Tomoki simply changes the subject to a supposed bug in Sohara's room. Sohara stupidly turns around to look for the bug, exposing her own panties to Tomoki (exactly what he intended). Cue big explosion in Sohara's butt, and Tomoki's evil laugh while taking cover from Sohara's attack. Doubles as a Crowning Moment of Funny.
Episode 9 even crosses this line with the infamous Tomoki Tower, almost taking the throne of the (even more infamous) Turtle Sequence.
The protagonist ends a bout of gratuitious wish fulfillment with the statement "Now all that's left is to take over the world!" in front of the Literal Genie Ikaros. The next morning, she has concluded that since no one would recognize him as sovereign, the most efficient way of granting his wish is to make everyone disappear. As in, every human in the world. And so she does. This is the first episode. They get better.
In the second episode, Tomoki starts shenanigans that leads to Sohara being unable to wear underwear. She beats him silly for it. When Ikaros shows up, Tomoki manages to croak "Panties..." She concludes that he wants panties, and makes every pair in the rear area fly off their owners and converge on Tomoki. This does not help at all.
Sacrificed Basic Skill for Awesome Training: Ikaros has combat & intelligence maxed out at the expense of her emotions, Nymph has intelligence & emotions maxed at the expense of strength and Astraea has sacrificed intelligence for strength & emotions.
Show Within The Show: That would be Barnyard Sonata, the soap that Nymph watches obsessively. It appears to take place on a ranch, and revolves around an illicit romance between the aristocratic Lady Umako and a burly farmhand. We don't get many details about other characters, although there is a powerful Count, and another character (not on screen) sounds as if he could be a talking horse.
Slapstick Knows no Gender: Tomoki occasionally hits Icarus (and even Astrea) on the head when they cause a lot of trouble for him. Like destroying parts of his house or flushing him down the sewer.
Slipknot Ponytail: When Nymph and Ikaros activate Pandora, they lose their pigtails/braid.
Something Else Also Rises: In episode 10 of forte when Ikaros sees Tomo making a kissing face through the TOMOKI Peeping Tom System she falls backwards and blushes heavily and her wings deploy.
Soundtrack Dissonance: A humorous version. Episode four's ending is a cover of a theme song to a war movie. Set against a backdrop of porn books.
Student Council President: Mikako. She has a bit of a devious streak, such as having life insurance set up to collect loads of money if Sugata fell to his death from hang gliding off the school building.
Super Drowning Skills: Basically all Angeloids, with exceptions being Ikaros, Siren, and Chaos. Though it's due in part to their wings absorbing water, and making them too heavy to float. Also, on the human side is Sohara.
Super Toughness: Tomoki. This guy make Kentaro look like a whimp. Hell, he had taken enough damage to cripple Superman for crying out loud.
Supporting Protagonist: Tomoki sort of fits this; although he's the center of the harem, and it's hinted at that he's The Chosen One, the drama is largely surrounded the angeloids, and the one who's actually trying to solve the mystery of Synapse is Sugata.
Suspiciously Specific Denial: In the first episode of Season 2, as the main characters are exploring each other's dreams, they come upon Sohara getting rather kinky with Tomoki. Sohara beats up Tomoki and Sugata (and tries to hit Mikako as well, but she dodges), then tries to pin these perverted dreams on Tomoki, but he keeps insisting these aren't his. She then decides to use a golf club to hit them away.
Sweet Tooth: Nymph. She holds candied apples in especially high regard.
Taking You with Me: Ikaros combines this with Taking the Bullet on a grand scale with Melan, the second generation type theta, when Melan shoots Apollon Ikaros takes the shoot and then activates her Aegis trapping both her and Melan inside its blast. Saving Tomoki, Nymph, and Astraea and defeating that copy of Melan.
Tastes Like Friendship: Tomoki does this twice, first with Nymph and a candied apple then later with Astraea and a full dinner at his house, along with a offer to feed her whenever she was hungry. Both instances of kindness eventually influenced their decisions to betray Synapse.
Teen Genius: Sugata and Mikako. They're well-versed in first-year college maths even though both are only 15. They might as well qualify as The Aces.
Tomoki's Angeloids form a set: Ikaros as the Wife (after she gained knowledge of everyday life, she leans towards this; also, she keeps a watermelon patch), Nymph as the Seductress (her attitude towards Tomoki after her liberation is leaning towards this), and Astraea as the Child (bumbling, ditzy, and quite innocent).
The girls in the Exploration club forms another unit: Sohara (Wife; she keeps Tomoki in line), Satsukitane (Seductress; she masterminds a lot, if a quite insane one), and Kazane (Child; she is quite na´ve, and ultimately thinks that this world is a game.).
Time Stands Still: One of the many powers Tomoki quickly abuses once he finds that reality can be altered on a whim. He also uses an invisibility cloak to peep on Sohara changing.
Title Drop: Episode 13 is called: "Sora no Otoshimono" or "Heaven's lost Property".
Turned Against Their Masters: Ikaros, Nymph and Astraea, thanks to the Power of Love and the fact that their human friends treat them as people rather than as crap. Daedalus and the Master both fear that Chaos will do this now that she has free will.
Undying Loyalty: Seems to be where the series is going. While Tomoki has been trying to free "his" Angeloids, the desire to obey a Master (to have one) is so intrinsic and necessary for the Angeloids well being, that the only thing he can do is become a kind, loving Master... who orders them to be free.
The Unsmile: Not really as bad as the other examples of the trope but Ikaros' "smiles" are just her going "SFX: Smile" with a perfectly straight face.
Wham Episode: Dear God, chapter 38. A truck hits Hiyori and kills her, which simultaneously awakens her Synapse counterpart and wipes her friends' memories of her. Nymph then reveals that there are more people who are dreams of Synapse's inhabitants.
As of Chapter 54, a new Uranus Queen Appears from the Sky Master. Tactical Angeloid Type Theta: Ikaros Melan. She has hurt Tomoki pretty badly as well
Chapter 55, Nymph's new form and Ikaros has PANDORA as well
the end of chapter 45. Chaos is back. Be very afraid. Especially after a second episode in chapter 47.
Chapter 70, After spending half the chapter running away from her attacks to the point that she lost her weapon and one of her wings, Hiyori sacrifices herself so Chaos can understand that hurting people is wrong...Nymph finds Hiyori broken due to Chaos' attacks and goes Unstoppable Rage while Chaos reveals herself to Tomoki as an Angeloid...
Nothing can possibly top chapter 73, the purpose of the rule is revealed by ikaros to start the world over, and thats literally what it does, as everything on the entire planet begins to breakdown and disappear, eventually the planet itself wil be destroyed and remade, people, animals, buildings, entire countries are wiped away completely..
It got worse in Chapter 71.Tomoki gets killed trying to stop Chaos and Nymph from fighting and effectively pushed Ikaros, Nymph, Astraea, Sohara, and Chaos full force into the Despair Event Horizon... with Chaos being emotionally shattered, leading her to run away and find Sugata, believing that he's the only person she can relate to, and knocks him out.
In Chapter 77, it's revealed that Daedalus, the creator of the Angeloids is — and always has been — the real Sohara Mitsuki, which explains how she knows all about Tomoki.
The Worf Effect: The hyper-competent Sugata, who can beat the crap out of wild bears, survive faulty flying machines with barely a scratch and outsmart combat Angels with Batman-like preparations, gets curb-stomped by Mikako in a wrestling match.
To a lesser degree, the Angeloids.
World's Strongest Man: It's... dubious how canon or serious this are in the continuity, but if we take the Tournament arc at face value Tomoki is the single strongest human ever, not only being capable of shrugging off Ikaros attacks (which brought down Astraea) but pierced Aegis with his Dong of thunder like it was garbage, literally knocking her down for good.