Doctor Who and his companions are hurled into the future and make a horrifying discovery: the Daleks have conquered Earth! The metal fiends have devastated entire continents and turned the survivors into Robomen.

Astronauts rescued from a mission to mars are kidnapped when they arrive back on earth. They seem to have been irradiated, and can now kill people merely by touching them. But the Doctor discovers the astronauts have been replaced with Alien ambassadors who are being forced to behave in a hostile manner. With The Doctor traveling to the alien mother ship, and Liz kidnapped, The Brigadier is left wondering who to trust.

The TARDIS lands in a space museum on Earth in the late 21st century, where the Second Doctor, Jamie and Zoe learn that contact has been lost between Earth and the Moon. In this era, instant travel — T-Mat — has revolutionised the Earth. Its people have lost interest in space travel. The Doctor and his companions travel to the Moon in an old-style rocket and reach the Moonbase, control centre for T-Mat, only to find a squad of Ice Warriors have commandeered the base and plan to use the T-Mat network to their advantage.

The TARDIS materialises in Earth's future on a space beacon just before it is attacked by pirates. The travellers find themselves trapped in a sealed section of the beacon. It is blown apart and flown to where the pirates will plunder it of the precious mineral argonite. They witness a conflict between the pirates and the Interstellar Space Corps, led by General Hermack and Major Warne. The ISC are convinced that the pirates' mastermind is an innocent yet eccentric space mining pioneer named Milo Clancey, while their true leader is a man named Caven. Caven has a secret base on the planet Ta. He is assisted by Madeleine Issigri, daughter of Clancey's ex-partner Dom, who - unknown to her - is now his captive. When Madeleine discovers Caven's full treachery, she helps to bring him to justice. The time travellers are given a lift back to the TARDIS by Clancey in his rickety old ship, the LIZ 79.

A murderer is examined by psychiatrist John Frame, who is surprised to find the criminal knows many details of his private life.

The population of the United Kingdom at the beginning of the 21st Century is static, thanks to computerised population control, but the wife of the Population Officer becomes pregnant for the second time.