Mel wants to go swimming so the Doctor takes her to a tower block called Paradise Towers where there is reputed to be a fantastic pool. When they arrive they discover that the place is far from being the superb leisure resort they had expected - it is run-down and dilapidated.
The hallways are roamed by gangs of young girls known as Kangs; the apartments are inhabited by cannibalistic old ladies, the Rezzies; and the building is managed by a group of dictatorial caretakers, presided over by the Chief Caretaker.
The latter is in thrall to the disembodied Great Architect Kroagnon, the building's creator, who is using giant cleaning machines systematically to kill all the occupants as he considers that they are spoiling his creation by living there.
The Great Architect eventually manifests himself by taking over the Chief Caretaker's body, but the Doctor and Mel join forces with the Kangs, the Rezzies and Pex - the only young man left in the complex - to defeat him. Pex, however, is apparently killed in the struggle.