Rhys having an... admirer in Katagawa makes sense when you look at his list of accomplishments, started out as a low-ranking "code monkey" yet was able to survive Pandora, single handedly brought down Helios (and likely took a chunk out Hyperion in the process), took part in a battle against a vault monster and won, looted said vault (alongside Fiona) and rebuilt the defunct Atlas corporation in only a few years. It's little wonder why he'd be a source of admiration (and possibly fear/envy) among people in other corporations. In addition, Katagawa's obsession with Rhys mirrors Rhys' own obsession with Handsome Jack, solidifying Rhys' position as Jack's Good Counterpart.
Early on, you give a damaged vault map to Tannis, who retreats into her little shack to attempt to fix it (the entrance is a black wall that keeps the player out), taking barely a few minutes to repair (somewhat, its still damaged but it works enough to display a single planet) what is essentially an alien artifact that Tannis herself admits most of the race's tech has stumped the brightest minds. With the reveal that Tannis is a Siren with the ability to Phaseshift (manipulate "anything with a current", i.e. electronics and machinery, possibly including the map), it might be possible that is what she used to repair it, as opposed to whatever research equipment she has in that tiny shack.
In Promethea, a side mission has you get some blood from a donor. Instead of using any sort of caution, or just hitting interact and having operation done normally, you instead have to hit melee and cut/bash the donors arm off. This could be a Call-Back to Borderlands 2, where Doctor Zed asks you to perform surgery by making a "small incision, just above the sternum", where you handle the situation in the same manner, to which he responds "close enough". Apparently, Vault Hunters don't make good doctors.
Tyreen's power to steal strength from others and give it to her brother is a corrupted version of Maya's Harmony skill tree, particularly Sweet Release and Life Tap. Let's all be glad Maya's a really nice person, or else there'd be two of them.
The monks of Athenas having a vow of peace and non-violence, as well as the history of the world having Siren rulers, goes a long way to explain why a single Siren like Maya was expected to dominate the entire planet through fear. It also explains why Maya was able to just kill the leader of the Impending Storm and walk away.
You may have noticed that the Nomad bandits from Borderlands 2 have disappeared, while most other bandit sub-types are still around. However, if you listen closely, you can still find them.... but they're now working for Maliwan as their Heavies. Considering the general psychopathy among the Maliwan soldiers you encounter, it's likely that many of their troops were recruited from bandits and criminals who were slightly more stable than the ones who joined the Children of the Vault.
In Greek mythology (references to which are everywhere in Borderlands as is), Typhon is a dragon with a hundred heads that Gaia, or Mother Earth, sent to defeat Zeus after he took out his father Cronus. Typhon and his mate Echidna had many monstrous children. What's this got to do with Typhon DeLeon, you may ask? Well, when you meet him later, he mentions that he has two kids, and that they grew up to be guess what? Monsters.
Also in Greek myth, Calypso was a nymph who kept Odysseus on her island for seven years. Her name comes from the Greek word meaning "to conceal/deceive." It's no coincidence, then, that the Calypso Twins did their fair share of deception in order to amass such a large following.
The names for the tattooed women, "Sirens", seems a tad non-indicative, as their powers never rely on voice and seldom hypnotize people (Maya's "Thoughtlock" ability is the only example). However, Tyreen makes it meaningful in a different sort of way. She and her brother manage to charm the bandits across the galaxy and frequently make use of propaganda centers and radio stations to spread their influence, all the while luring many of their followers to their death for sustenance.
In much the same way that the second group of vault hunters seemed to outclass the first, the current crop seem much more capable and experienced, both in character and mechanically. This would explain, for instance, the greater degree of customisability of action skills and augments, whereas previous vault hunters only had one.
Lilith's Siren abilities were largely self-taught and Maya received some instruction but only from a group of monks who wanted their own pet superhuman and so probably didn't tell her everything she could do. On the other hand, Amara has been making constant use of her siren power for years as a vigilante. Self-taught or otherwise, she trumps both previous sirens in sheer experience, explaining her versatility (her three base abilities) and being able to alter the ways they work (the augments and elemental modifiers).
Axton was a professional soldier, sure, but a bit of a maverick and loose cannon by the sounds of some of his ECHO logs. Moze on the other hand, was part of an elite squadron of mechanised infantry with a fearsome reputation and retains her soldier's discipline (mostly) all of the time.
"Jack" AKA Timothy Lawrence was just some poor schmuck randomly chosen by the real Jack to be his body double. While he proved to be a very capable fighter, he was thrown in at the deep end and cannot compare to Zane (who he is most similar to,) a seasoned-veteran and professional hitman.
FL4K is the hardest to pin down: They are likely self-taught as Mordecai was, the only difference being their robot brain could help them learn a lot faster, plus their background as an archivist bot could give them access to all the information they need on the creatures they tame. Word of God also states they are several hundred years old, giving them more time to learn.
Why do the Children of the Vault rename themselves the Children of the Firehawk and (maybe) stop being so viciously psychotic? For the duration of the game they'd been worshiping Tyreen who called herself a god and would kill her believers at the drop of a hat and for no reason. Lilith, on the other hand, managed to stop the apocalypse the Twin Gods had started, plus branded Elpis with her logo, marking her as more powerful than Tyreen and Troy in addition to saving the COV members. She's stronger and benevolent - much closer to a god worth the worship.
For gameplay purposes, however, the COV are still fought in the post-game. Their radio broadcasts proclaim that they will continue to fight in Tyreen's name no matter how badly they're beaten down.
Maliwans prescence on Nekrotafeyo would explain a lot of things - mainly, the new, almost alien like design of their guns, as well as the ability to shift between two elements. Rhys claimed that the research benefits of studying a mere Vault Key fragment would have kept Atlas afloat for potential decades. Now imagine what Maliwan could do (and probably did) with a whole planet full of potentially still functioning Eridian technology.
Early on in the game, when the Vault Hunters arrive on Promethea, it's revealed that the Calypsos are already there, and have been, as Tyreen said, "for ages". It's the same story with Eden-6. And whilst on Promethea, you get a call from Tyreen wherein she indicates she was about to drain an entire newly-pledged bandit clan of their energy, seemingly for shits and giggles. But that's exactly it - she wasn't draining huge swathes of her followers just to satisfy her hunger. She was using them as fuel, probably along with some Eridium, to teleport entire armies from planet to planet with Liliths powers!
Also, on Eden-6, most of the bandits come from the population of the prison. An ECHO recording from Clay indicates that the prison gangs had already sworn allegiance to the Children of the Vault long before the Calypsos arrived and left Wainwright as the heir. The rest of the bandits were teleported in later by Tyreen.
The absence of the Borderlands/Pre-Sequel Vault Hunters from previous titles - those who are still alive or not working for the Calypsos like Aurelia anyways - may be a bit odd, given that a threat this big should warrant them all being pulled in, but besides the fact that this is a new Borderlands installment and thus new heroes are required, it's been seven years, long enough for everyone to have moved on from the Crimson Raiders. After all, Jack and Hector are dead, their respective armies crushed and scattered to the four winds, so naturally, it'd make sense for the Borderlands 2/Presequel Vault Hunters to put down their guns and go do something else for a change, which conveniently leaves (most) of them far from the events revolving around the Calypsos. And going by the games and their respective personalities...
Axton, being a model, is likely somewhere far from the frontier worlds the story takes place on, and his absence from a developed world like Promethea can be explained in that he never met Rhys, and while he might still be in contact with Zer0, his occupation as a model means he's either done with or disinterested in the concept of jumping into another firefight to save a planet that routinely attempted to murder him on a daily basis.
Gaige is an outlaw who specifically went to Pandora to get away from the law, and an Echo log found in-game indicates the Holloways are still chasing her. She may have accordingly chosen to have left to protect the Crimson Raiders from getting involved with the feud she has with the Holloways, which she may see as a personal thing that she needs to handle by herself, as opposed to dragging the Raiders into it and escalating the feud into some kind of a war. She returns in the Love, Guns, and Tentacles DLC , and now works as a wedding planner.
Seeing as he's a bit of a family man, Salvador may be off visiting his beloved Abuela, and given that he's not exactly the most responsible of the Vault Hunters, if he was given a method of contact, he likely lost it. That, or is penchant for chaos means he's simply gone off to go trash things somewhere else.
Athena is likely off somewhere attempting to live a peaceful life with Janey.
Timothy, having gone into the movie business, is probably busy filming whatever movie he's busy filming, and thus unavailable due to his shooting schedule. At some point during his career, he got trapped in the Handsome Jackpot casino, and he remains there until this game's Vault Hunters free him.
Krieg's primary motivation for joining the fight lay in wanting to exact revenge upon Handsome Jack, and because he liked Maya. Given that Jack is dead and Maya has moved on from the Raiders, he has no reason to stay with them. That, and he's a psycho, the kind of person the Raiders shoot on a daily basis. Assuming he didn't leave of his own volition, without the other Vault Hunters with him to keep his homicidal urges pointed in the right direction, he would've probably become very unwelcome sooner or later.
Of all the bandit types why haven't the Rats been recruited into the COV? Apparently the Calypso Twins found them too creepy to work with. That and they're skin and bones, not much for Tyreen to feed off of.
The logic of the weapon manufacturers and what they make and the changes made between the last game and this one:
Atlas: With Rhys in charge, their handguns and rocket launchers are now wrist-mounted. Their assault rifles still require two hands to use though. All 3 weapons come with alt-fire trackers that lock-on to the enemies. Submachine guns wouldn't benefit much from homing trackers and bullets, nor would shotguns or sniper rifles, hence their absence in Atlas manufacturing. However with one exception most of their guns don't have any elemental enhancements at all as the grenade mods fill that niche. This is due to Maliwan and the COV invading Promethea, which no doubt interrupted any attempts to enhance their firearms with elemental powers, given that there's a planet-wide invasion going on.
COV: They still don't make sniper rifles, for the same reason as their bandit predecessors; their troops have neither the discipline, patience or tactical acumen to wield them effectively. COV guns drawing ammo from the backpack effectively eliminates manual reloading, allowing their troops to fire non-stop...which is basically their one and only strategy in combat. However, this comes at the cost of overheating and repair if the guns ever break, hence the need for spare parts and water bottles, squirt guns and portable hoses. Also they had to abandon their shotguns and SMGs, probably because they didn't mesh well with the More Dakka philosophy being bumped Up to Eleven. You can imagine the bandits not being happy about this, as it hinders them to some extent in close range, which, admittedly, is somewhat made up for them retaining their trademark Action Bomb and Close Quarters Combatant tendencies.
Dahl: They still make pistols, SMGs, sniper rifles and assault rifles - pretty straightforward military gear, but precise military gear. Dahl prizes accuracy and minimal collateral damage. However after receiving complaints about their guns being restricted to aim at the sights to bring out their full potential, and after no-doubt witnessing first-hand (via the events of 2 and the Pre-Sequel) what happens if people armed with their weapons get caught at ranges where the fire-mode is ineffective, the company decided to install alt-fire modes to their weapons. Now Vault Hunters can burst fire or go full automatic at both the hips and sights!
Hyperion: After having their asses handed to them by the Vault Hunters and Handsome Jack's demise by said Vault Hunters, Hyperion decided to make some changes to distance themselves from their tenure under Jack. First off getting rid of handguns due to their awkwardness, lack of real killing power despite their accuracy, and just being associated with Jack as the weapon that murdered a renowned Vault Hunter. Second, adding shields while aiming to their shotguns, SMGs, and sniper rifles no doubt helps their intended audience - the corporate layman, of whom is likely neither heavily armored nor particularly battleworn - survive in Borderlands' cutthroat corporate world. Finally shoving the Jack A.I. into an SMG and installing Tediore firmware diversified the company's portfolio, going from being the guns that were the most accurate to guns that are more adjusted for the dynamic battlefield.
Jakobs: No rocket launchers or SMGs, entirely for aesthetic reasons. Their old school of thought - extremely high damage, critical modifiers and a strong emphasis on sheer damage over everything - remains unchanged. However some of their purple quality or higher assault rifles are now hand-cranked - referencing the early Gatling Guns - and any critical hit made by their weapons will have the bullet ricochet to the next target, allowing a skilled marksman to make the most of their shots. Their shotguns also have the potential to possess larger magazines, likely due to Wainwright's preference for them given his disability.
Maliwan: No assault rifles, as per tradition, but they have dropped the rocket launchers for shotguns, likely to fit in with their "stylish corporate executive" aesthetic. Maliwan build weapons to make their designers feel clever, after all, which means either weapons that are precise (pistols, sniper rifles) or weapons that let them push the boundaries, with their tech submachine guns as a speed test. With Katagawa in charge of Maliwan, the rocket launchers were dropped in favor of shotguns as he felt that shotguns give the enemy a personal sense of fear. That and he was probably tired of hearing complaints from Torgue.
They also added in alt-fire elemental capacitors like incendiary/shock to deal with enemies that have shields or incendiary/corrosive to those who have armor, likely as a result of finding out the hard way that having a powerful elemental weapon means absolutely nothing if the opponent in question can No-Sell the oncoming fire.
Tediore: After having their asses handed to them by Vladof's Iron Bear Corps, Tediore decided to make changes to their reload system. Instead of being simply grenades, they become turrets that fire down on the enemy or drones that hunt down their prey. However they had to abandon their rocket launchers for this feature to work and other companies still see Tediore as a joke though they won't be laughing as much when a horde of Baby Maker and Smart Gun XXL drones move in for the kill.
Plus, the newfound diversity of Tediore means that they have something other than being a very cheap brand to buy from and their dubious honor as useful Vendor Trash going for them. Their guns having a wide range of gimmicks and abilities means that people who would've either passed them over or sold their weapons to the nearest vendor the moment they had the opportunity will now be taking them seriously when picking out weapons to carry into battle.
Torgue: No submachine guns or sniper rifles still apply here. When Torgue was reinstated as the company face he was forced to compromise by having weapons get elemental enhancements since explosive damage is no longer considered an element and the new radiation element could fill the niche of making things explode. On the other hand having sticky gyrojets alt-fire on your rifles, shotguns and handguns is perfect due to enemies having a nasty habit of escaping your line of fire, and the gyrojets mean that there's not much they can do once an explosive bullet is latched onto them. Apparently Jakobs liked the idea as well when they created The Duc pistol based on Torgue firmware.
Vladof: No shotguns or submachine guns also still apply here. However after the Darzaran Bay Massacre (which unbeknownst to the company Moze was the sole survivor), Vladof decided to make changes by adding more firepower to their weapons so incidents like that never happen again. For their alt-fire modes, we have zip rockets, tasers, grenade launchers, rocket launchers, mortars, double-barrels, and shotguns. As a matter of fact, Vladof created the Sickle, an assault rifle with shotgun properties as an homage to their discontinued Hammer shotgun from the first game.
All of this also makes sense when one takes into account that Vladof - like every other company - has learned from the weaknesses of Crippling Overspecialization that were demonstrated in the first three games. More Dakka, while effective, will only carry the company so far, so their subsequent foray into all sorts of under-barrel attachments is at least rooted in making their weapons more competitive with the other companies.
Cryo and Radiation deal decent damage to both armor and shields respectively though not as much as corrosive and shock. Why? Prolonged exposure to extreme cold can make armor brittle and radiation can interfere with electronics which shields are made out of.
On a similar note, beside the fact that the other elements are more effective, Slag's absence from the game is quite simple. Jack's Hyperion had a monopoly on Slag weapons due to their extensive work with Eridium. With Jack dead, his incarnation of Hyperion burned to the ground, and Pandora no-doubt having a reputation as being a graveyard for any corporation that dares set foot on it, Slag in a weaponized form simply doesn't exist anymore, since no one's around to research Eridium and weaponize the byproducts.
Atlas and Jakobs are among the few weapon manufacturers who side with the Crimson Raiders. Coincidentally, both of these companies tend to ignore elemental attacks, save for a few unique examples. Meanwhile, the villain company of the week is Maliwan, who specializes in only elemental weapons.
Additionally, the CE Os that work for those respective corporations have good reason to ally with the Vault Hunters. Besides the fact that the Crimson Raiders singlehandedly-ish save him and his company from utter destruction, Rhys has history (most of it positive) with the Vault Hunters, almost all of whom were affiliated with the Crimson Raiders. Similarly, Wainwright is romantically involved with Alistair, a longtime friend of the Crimson Raiders. Even without witnessing the heroic actions of the Crimson Raiders first-hand, both CE Os have spent plenty of time with people who were affiliated with them in some way, and therefore should have a good idea of the Crimson Raiders' mandate.
Kill-a-volt is likely using the Transformer shield himself, being completely immune to electric attacks, hence his higher drop rate of said shield.
Alistair Hammerlock seems like a perfect match for Wainwright Jakobs, being a hunter with a preference for sniper rifles and precision shooting, which no doubt compensates for Wainwright's crippled eyesight. It helps that Alistair also made use of Jakobs weapons before meeting Wainwright, as shown in the Big Game Hunt pack in the previous game.
Aurelia Hammerlock being a villain under the employ of the Calypso Twins makes sense when you remember that she was part of the villainous half of the Pre-Sequel's Vault Hunters, but unlike Nisha and Wilhelm, she lacked any loyalty to Handsome Jack and Hyperion, sparing her from death for a while when Hyperion made enemies. Only the chance to spite her brother gave her the push to become a target of the Crimson Raiders.
The Mayor of Trashlantis giving you only cosmetic items for completing his share of optional map-specific searches, as opposed to Torgue's and Ember's equivalents, makes perfect sense when you remember his stance against corporate greed, and the fact that he is a tailor.
Gaige's wholesome support of the marriage between Hammerlock and Jakobs makes sense when you remember that Jakobs weapons, with their modest magazines and potentially fast firing rates, were ideal for building Gaige's Anarchy boosts.
In the research logs, Eleanor and Victor never use the word "Eridian," only referring to "precursors," even though the ruins are clearly Eridian and Gaige conclusively identifies them as such. However, Eleanor and Victor are a lot older than they look; Gaige notes that all their tech is so old she's barely even heard of it, and she's a bit of an old tech nut. It seems like they were some of the first people who found Eridian technology, before that word had even been invented.
Just outside the Holy Broadcast Center, you can find a derelict bus with graffiti on it. The graffiti depicts 6 silhouettes labeled "Vault Hunters", and four of them are crossed out. Taking into consideration that only two of Borderlands 2's Vault Hunters make a physical appearance, the implications are disturbing.
This is one is slightly lessened by the fact that this graffiti is a Recycled Asset from The Pre-Sequel!! (See the bandit truck from the opening cutscene.) Adding to this, Borderlands 2 establishes that the Vault Hunters we see are not the only ones out there (Handsome Jack is said to have killed many before the start of the game.) So while our Vault Hunters may be okay, this just means that many others didn't make it.
With the exceptions of Salvador, who is unaccounted for, and Maya, who is dead as per the storyline of 3, the Borderlands 2 Vault Hunting team is strongly suggested or outright confirmed to still be alive, given that Axton has apparently retired from frontline service as a Vault Hunter and taken up a day job as a model, Gaige is still being hunted down by the Holloways while working a regular job as a wedding planner, Krieg is apparently still wandering Pandora and is now sane enough to hold a coherent conversation and Zer0 is working for Rhys as his personal bodyguard.
One of Typhon's logs points out that a lot of ships crashed on Eden-6 like something was attracting them. When you fight the Graveward, note how one of its arms has rocket boosters and you may have a reason why.
Ava's actions in the first vault leads to a chain of events that nearly let the Destroyer free. Had she not been in the vault, Maya wouldn't have grabbed Troy. If Troy hadn't been grabbed, Maya would never be leeched, and the twins wouldn't be able to Phaselock Elpis and try to set the Destroyer free.
However, it was Typhon DeLeon's Deconstruction of Overprotective Dad that made the Calypso Twins into who they are which led to the events of the game. Typhon may have been the first Vault Hunter but he was still human.
The people of Elpis, including the citizens on civilized settlements like Concordia, were likely obliterated in a cataclysmic event when the Calypsos phaselocked the entire moon and dragged it close to Pandora. Even if there were survivors, then Lilith blasting herself onto the surface and searing a fiery phoenix would have immolated half the moon's population.