Four of the six episodes are missing.
In 2011, 2020, and/or 2079 (that's how much they cared about consistency in 1960s Doctor Who—whatever, it's all the distant future), the TARDIS lands on a spaceship, and the Doctor and Jamie are immediately attacked by a servo robot. Jamie uses his mastery of technology to radio for help, and some people from a nearby space station rescue them. The space station is round, and it spins, almost like a wheel in space.
Then, Cybermats! They sneak onto the station after the Doctor and Jamie, and begin secretly preparing for some kind of secret invading force. I wonder who it'll be? Zarbi?
We meet the space station's crew, who include people from every country on Earth, all played by white English people with bad accents and makeup, and the woman in charge is less progressive than it sounds once you remember that every base commander in Doctor Who is dangerously unstable and will ultimately cause more problems than the monsters. But still, they're pretty good characters with believable interactions, not just racist stereotypes to prove how multiculti the BBC is.
And of course one of them is Zoe, a brilliant astrophysicist and also parapsychologist and I think she has a different job the third time they mention her, but she's actually a student majoring in pure maths. Her description of how training works in the 21st century is actually pretty dystopian-scary in the way Blake's 7 always wants to be but rarely is. Then she laughs at Jamie's skirt, and he talks about spanking her, but we never get to see that.
The space station people want to blow up the spaceship, which would actually prevent all the problems they don't know about yet and end the story early. The Doctor and Jamie don't want that, because the TARDIS is there, but they refuse to tell anyone why, so nobody listens. So Jamie sabotages the station's X-ray laser. Then it turns out there's a meteor shower that's going to fuck up Earth, and they need the X-ray laser for the that. Oops. The Doctor needs his vector generator rod from the TARDIS to fix it, so Jamie and Zoe put on Bossk's spacesuit from Empire Strikes Back and head back to the spaceship to get it. Later, the crew somehow fires the X-ray laser at the meteors anyway, and Jamie and Zoe almost get shot, but don't.
Meanwhile, the invaders have invaded, and they are Cybermen! Just two of them, which is barely plural, but still, these Cybermen actually look dangerous, and they finally have the teardrops that they'll keep through the next 300 redesigns. And it's kind of cute that the two Cybermen let you know which one's talking by bowing like a Japanese businessman. They aren't susceptible to gold, but instead to quick-setting plastic. Good thing that's what Jamie found and used to sabotage the laser, and kept around somewhere in the pockets he doesn't have.
The Cybermen recognize the Doctor and plan to lure him somewhere he can be destroyed, but he escapes. So they kill a few people and hypnotize the rest, and reveal their plan: They will use the radio link between the space station and Earth as a Cyberbeacon to guide their massive Cyberfleet, who otherwise wouldn't be able to find a planet zillions of times bigger than the space station they just found with no problem. And then they poison the air supply so everyone will die and nobody can turn the beacon off.
The Doctor unhypnotises most of the crew, but there's some tension about who's still hypnotised. He fixes the poison problem by switching over to sexual air supply.
Jamie and Zoe return with the Doctor's rod. He not only fixes the laser, but soups it up into a super death ray, which he uses to genocide the Cybermen. There are a couple of Cybersurvivors on the space station, but the Doctor makes sure they get flushed out to space and die a horrible death. His final solution complete, he rubs his hands and smiles the smile of a man who never wouldn't.
Two of the people on the station fell in love while the story was happening. Yay for them.
Zoe tries to stow away about the TARDIS by hiding in a locker, but the Doctor catches her. He tells her if she can watch The Evil of the Daleks without hiding behind the sofa, she can come. Jamie grumbles about it because he's still pining for Victoria, but after Zoe turns away from him he decides he doesn't mind having her around for some reason. So, for the next 7 weeks, everyone gets to watch Zoe watching that story while the cast and crew take a much-needed break. This unprecedented repeat costs nothing and gets good ratings, so to make sure that never happens again, the BBC wipes the tapes.
ReceptionEditDespite the great visuals (for 1968, except for the meteor storm) and unique sound (the first all-Radiophonics incidental sound, so they're experimenting a bit), this is often called the worst Second Doctor story. And if you watch the reconstruction (actually one of Joint Venture's best recon jobs) or listen to the audio version, there really is a whole lot of padding, and some nonsensical plot developments. Also, Whitaker clearly hadn't figured out how to make Zoe work as a companion yet. And some egregious bits of Kit Pedler thinking he's a physicist rather than a physician and giving them hard-SF subplots that are laughable.
But fortunately, the BBC has fixed things for you by erasing all that padding. You can just skim the plot and then watch the final episode (one of the two that exists), and it's actually pretty cool that way.
Much of the plot actually happens in that episode anyway. And with only 25 minutes, you have enough time to be impressed by how well-realized and believable the crew and their relationships are, but not enough time to notice how boring they are, and Troughton seems like he's doing an amazing job playing "Second Doctor exasperated at everyone's stupidity" if you don't notice that he's like that for 6 weeks straight because they delayed his vacation.