The one where the Doctor makes the "Daleks can't climb" joke.
Is there a stowaway aboard the TARDIS? No, it's just Romana, who has regenerated off-screen, for no apparent reason, and has chosen to do so into an identical double of Princess Astra. The Doctor tells her to pick something better, and she shows off several more very alien bodies (none of which meet the Doctor's approval either) before returning to the one she started with. (The Doctor Who Expanded Universe has made several attempts to explain why Romana regenerated, as well as how she was able to change her form several times without wasting regenerations. Few make real sense.) Also, K-9 comes down with a case of robot laryngitis and stays in the TARDIS for the rest of the adventure.
Meanwhile, the TARDIS has arrived on a seemingly deserted planet that the Doctor finds naggingly familiar. It's Skaro, home planet of the Daleks. The Doctor last visited it five seasons ago, when he crossed metaphorical swords with the Daleks' creator, Davros. The Daleks have also returned, looking for their creator; they'd left him for dead when they decided he had outlived his usefulness, but now they've found a new use for him.
The Daleks' problem is that they've reached a stalemate in a war with the human-looking Movellans, and need Davros to cast a fresh eye on the problem. Speaking of Movellans, there's a group of them come to find out what the Daleks are up to, and when they find out they decide that if the Daleks are taking advice from Davros, they'll take advice from the Doctor — whether he wants to give it to them or not.
The Doctor teams up with La Résistance and very gleefully plays cat and mouse with Davros for a while. Romana gets herself kidnapped by the Movellans, who turn out to be not human at all, but a race of robots led by a central computer. They're locked in a war with the Daleks, and — as the Doctor points out — the two sides are so logical that they can always perfectly anticipate each other. They need a random element, which the Doctor happily provides by annoying Davros some more. He defeats a Dalek with his hat (by putting it over the eyestalk), and pushes Davros' only remaining hand down on the big red "blow up the entire Dalek suicide squad" button. He and Romana high-tail it off the planet very quickly.
This story was a turning point for the Daleks, for better or for worse — every Dalek story for the next decade was more of a Davros story with some Daleks in it than an actual Dalek story, and the Daleks themselves would be more disposable flunkies to Davros.
The Daleks in this story are also a bit more on the Straw Vulcan side than usual, and Adams insisted on calling them "robots" and "computers" a lot. A Dalek without its casing is encountered by the Doctor, though, and the episode does emphasize that they're a living race, so it can be assumed that Adams just really liked the word "robot".
- Achilles' Heel: The major weakness of the Movellan design was each android's external power pack which, being carried on their belts, was easily removed and completely shut down the android, not to mention they could easily be modified, reprogramming the android to obey human orders.
- Air-Vent Passageway: The Doctor and Romana use one of these to escape the Daleks, which gets not-so-subtly lampshaded.
- BBC Quarry: Mocked by the Doctor. "Oh look! Rocks!"
- Big Little Man: Romana is trying out different bodies into which to regenerate, while the Doctor is crouched on the floor fixing K9. Romana reappears as a silver-skinned alien babe, towering over him.Romana: "I thought I'd try this one, but it's a bit short."(The Doctor stands up, revealing Romana is the size of a child)Doctor: "Well lengthen it then, go on."(Exit Romana. The Doctor crawls along the floor for a while and then bumps into a toga-wearing beauty. He stands up...only to find he only goes up to Romana's shoulders)Doctor: "Too tall, take it away!"
- Black and Grey Morality: The Daleks are fighting the Movellans, who don't really appear to be all that much better than the Daleks because they were prepared to cause Skaro's atmosphere to spontaneously combust without any apparent concern for the fact that there were plenty of innocent people still on the planet who would have been incinerated by the resulting firestorm. The Movellans are only better by virtue of not being Absolute Xenophobes - they come across as indifferent to other species (albeit perfectly willing to use them to their own advantage), rather than trying to wipe them all out. At one point they even mention that they were perfectly willing to conquer the galaxy themselves once the Daleks were out of the way.
- Can't Use Stairs: This trope is referenced directly as the Doctor taunts a Dalek:Doctor: "If you're supposed to be the superior race of the universe, why don't you try climbing after us?"
- Cliffhanger Copout: It looks like it's curtains for Romana in one cliffhanger as she is trapped in a containment tube with a bomb ticking down. Next episode the bomb reaches zero and doesn't go off. Agella then reveals the bomb was never armed and thus Romana was never in any danger.
- Costume-Test Montage: Romana gets one.
- Deadpan Snarker: Romana and the Doctor keep it up even when the Doctor is pinned under a large rock:Romana: Don't go away, will you?Doctor: I'd rather hoped you'd resist the temptation to say that.
- Deceptively Human Robots: The Movellans outwardly resembled physically attractive Humans of various ethnicities and both genders. All of the Movellan androids wore white, form-fitting uniforms and their hair in silver braids resembling metallic dreadlocks. Being androids, the Movellans were stronger than humans. Because they do not wish to reveal their mechanical status to others, they do not allow aliens to see them in death, claiming such a thing would be against their code of honour.
- Distaff Counterpart: Post-regeneration Romana not only acts more like the Fourth Doctor than her predecessor, she even dresses in a feminine version of his costume.
- Dropped a Bridge on Her: Romana regenerates undramatically, and for no apparent reason, in the first scene.
- Evil Cannot Comprehend Good: The Doctor ends up in a Mexican Standoff with the Daleks. He is threatening to destroy Davros with a bomb unless they let him leave with his captive, but the Daleks respond by bringing in several human captives and exterminating them one by one until the Doctor surrenders. He threatens to set off the bomb right on the spot, but the Daleks argue that such an action would be irrational and impossible because it would kill the Doctor as well. Davros tells them that the Doctor is actually willing to do just that since "his logic is impaired by irrational sentiment".
- Facepalm: Romana makes this expression when the Doctor says that Davros' intellect rivals his own.
- Faking the Dead: Romana uses her ability to stop her own hearts in order to escape from slavery by faking her own death. Earlier, she had been told that "the only way to escape the Daleks was to feign death."
- Finger-Twitching Revival: Twice!
- Forever War: The Daleks and the Movellans are locked into one that strangely has a zero body count. Because their tactical computers are totally logical and perfectly matched, they're stuck eternally maneuvering for position without ever being able to actually commit to an attack. Davros and the Doctor independently come up with the same solution: turn off the tactical computer and do something illogical, which the other side's computer can't expect.
- Hand Wave: K-9 sits out the adventure in the TARDIS with robot laryngitis.
- Hypocritical Humor: During Romana's regeneration scene, the Doctor talks about how it's "what's inside that matters," yet he rejects each of Romana's prospective bodies purely due to their appearance. When Romana comes out dressed exactly like him, he applauds her newfound sense of style. Romana, of course, calls him out on this.
- Human Popsicle: Davros becomes one.
- Lampshade Hanging: "Oh look, rocks!"
- "How can a robot catch laryngitis? I mean, what do you need it for?"
- Lie Detector: The Daleks use one while questioning Romana.
- Lighter and Softer: Compared to the last Dalek story, this one is much more comedic.
- Magic Countdown: The countdown for the Nova Device tends to jump around quite a bit during the third episode cliffhanger. Then in the following episode it hits zero and then rolls over to 9999 - the device wasn't armed.
- Male Gaze: When Agella blocks the Doctor's path in the ruined Dalek City, we are treated to a close-up of her rear.
- Mexican Standoff: A squad of Daleks corner the Doctor, but he threatens to blow up Davros if they don't "spack off!" When they do stand down momentarily, the Doctor says "I believe this is what's called a Mexican Standoff".
- Mood Whiplash: It's pretty obvious where Terry Nation ends and Douglas Adams begins. Dark scenes (the Daleks executing prisoners) are followed with comedic scenes (the Doctor making fun of Davros).
- The Nth Doctor: Romana becomes only the third Time Lord in the show's run — the first obviously being the Doctor, and the second K'Anpo/Cho-je — whose regeneration we actually get to see, albeit only part of it and leaving out Mary Tamm.
- Not Quite Dead: Davros, who was saved by the backup functions of his life-support system.
- Oh, Crap!: The Doctor's reaction when he finds out he's on Skaro.
- Plot Hole: Romana's regeneration comes absolutely out of nowhere, is (as far as anyone can tell) not even remotely linked to anything we know about regeneration, and was subsequently never mentioned again. In fact, later writers went out of their way to establish that regeneration does not work that way.
- The Tenth Doctor's later explanation about a Time Lord's physical form being slightly malleable post-regeneration is generally accepted by the fans as a halfway decent Hand Wave as to why this could happen. At least, as to why the body montage isn't wasting her regenerations for a gag. There's still no knowing what caused her to regenerate.
- Real Life Writes the Plot: K-9's sidelining due to robo-laryngitis. Sources differ on to why exactly this happened some say it was because Terry Nation hated K-9 and didn't want to "degrade" his Daleks by making them appear with K-9 on-screen, while others have said that because of the amount of quarry filming in this episode, there was no way that K-9 would ever have been able to play a major part in the episode.
- Recycled Soundtrack: Skaro sounds from "The Daleks" can be heard.
- Ridiculously Human Robots: The Movellans.
- RockPaperScissors: Used by the Doctor and Romana to show the Movellans the fallibility of fighting only with logic.
- Shout Out: The Doctor reads a book by Oolon Colluphid. (Douglas Adams was the script editor for this season, and probably added that bit himself.)
- Straw Vulcan: Both the Daleks and the Movellans.
- Strong as They Need to Be: While Gallifreyans are depicted as tougher than humans in some ways, being somewhat stronger is something not often touched upon. Romana provides an example during a struggle with a Movellan over a detonator switch, where she kicks his arm hard enough that it tears away at the joint. At the end of the episode both Time Lords are digging out the TARDIS and tossing boulders larger than themselves (perhaps another BBC Quarry gag as the debris includes an inexplicable steel truss).
- Suicide Attack: The Daleks attempt one.
- Tears of Fear: When Romana is interrogated by the Daleks.
- Unusual Euphemism: The Doctor tells the Daleks to "Spack off!" when he's threatening to blow up Davros. (This was Tom Baker messing up a line, but it's entered into Doctor Who history as a particularly vicious Gallifreyan insult.)
- Weaksauce Weakness: The Movellans can be killed by removing the unprotected power pack on their waist. Daleks can apparently be blinded by hanging a hat over their turret stalk, which serves as their eyes.
- We Will Use Manual Labor in the Future: "Humanoids are effective work machines!"
- Wrong Genre Savvy: Davros apparently still thinks it's the Hinchcliffe era, and that the story is another grim Nazi allegory. In the far Lighter and Softer Williams/Adams era, he ends up coming across as an overblown idiot rather than a dangerous villain.
- The X of Y: The title, which the story at least tries to make relevant by having Davros rant about destiny several times.