After journeying back in time to see the living museum pieces of the Crusades - Richard the Lionheart and Saladin - the crew of the TARDIS arrive on a mysterious planet where they risk becoming very not-living museum pieces themselves. This exercise in eschatological dread is the fifteenth story of the original Doctor Who, The Space Museum.
The mystery hits them from the very beginning, when something jars the TARDIS mid-flight and land on a silent planet. More mysteriously, they have inexplicably changed from their 13th century outfits to their normal wardrobes. In the process of retrieving a glass of water for the Doctor, Vicki drops it to the floor where it smashes... and immediately reforms and leaps back into her hand. Somehow, Ian, Barbara, Vicki and the Doctor are being preserved.
Leaving the TARDIS to investigate the collection of antique spaceships surrounding them, they discover a dead world covered in a thick layer of dust. Furthermore, it is a layer of dust into which they can leave no footprints. Even more disturbing, they find that they are incapable of touching the artifacts. Not because of a pane of glass or force field, but because their hands phase right through them. This is truly the stereotypical museum from Hell: not only are they surrounded by boring case after boring case of untouchable artifacts, but the museum is so hostile to visitors that even the layer is dust is protected against them.
This ambivalence towards the preservation of history in museums reaches a fever pitch of horror when the crew discover the TARDIS amongst the collection. Looking around the display, they finally see themselves, in perfect preservation, as specimens locked away under glass. The Space Museum is not only a screed on museums, but an acting out of the angst that we ourselves will one day become history. Just as we gaze upon the pottery and arrowheads of antiquity, so too shall someone sometime in the future be looking upon our own laptop computers and cellular phones as the artifacts of a primitive culture. Not only do we groan at boring old history but, if we dare contemplate it, we will ourselves becomes some other poor soul's boring old history.
The assault on museology continues as the quartet try to escape the Space Museum and the fate awaiting them, only to get hopelessly lost in the winding corridors. Meanwhile, the hunt is on as the agents of the Morok Empire and the native Xerons each try to enlist the aid of the visitors. When the good Doctor is captured, he receives a speech from the curator that reflects the imperial plunder of England's own museums. The Space Museum exists to showcase the glories of Morok conquest, though in the waning days of their empire few care to bother with such dusty cases of artifacts. The museum is a rather empty place.
This dread over the inevitable encroachment of history segues into a meditation on fate. Having seen their future selves locked up as museum exhibits, the Doctor, Barbara, Ian and Vicki are stuck questioning their every move in the effort to avoid their own destinies. It is fine enough for the Doctor to harangue Barbara over trying to change the distant past of the Aztecs... it suddenly takes on much more immediate interest when one has seen their own future. Throughout, they must agonize in second-guessing themselves, and in the end wonder whether or not they actually did change their futures.
In the course of investigating the Space Museum, the crew also comes across the shell of a Dalek preserved as an exhibit. This delights Vicki no end, as she's only read in history books about the Dalek invasion of Earth some 300 years in her past. The Doctor, Barbara and Ian remark that they were there and that she wouldn't be so delighted if they ever meet up with the Daleks again. Unfortunately, that encounter comes sooner than they could ever expect.