The Enterprise diverts from its current heading and answers a distress call asking for medical attention. When they arrive at the planet Kirk discovers a group of individuals who claim to have visited Earth during the time of the great Greek philosophers, Plato and Socrates. They plan to get McCoy to stay to lend his medical expertise... no matter what it takes.

The TARDIS is in need of repair, but when the Doctor tries to track down an old friend for help he falls into the hands of Tobias Vaughn, the megalomaniac CEO of International Electromatics. The electronics company is under observation by the United Nations Intelligence Taskforce, a new international military team for fighting threats from beyond the Earth - headed by the Doctor and Jamie's old friend, Alistair Gordon Lethbridge-Stewart (promoted to Brigadier following the Yeti invasion). Vaughn is in league with aliens who intend to invade Earth, but he intends to betray them and seize control; however, as insurance should his plans fail, he wants the Doctor's TARDIS. When Vaughn kidnaps Zoe, the Doctor requests UNIT's help to rescue her - but their interference forces Vaughn to advance the invasion schedule, leaving the Doctor with little time to mount a defense... and the situation becomes more urgent when the Doctor realises that Vaughn's allies are the Cybermen, and that their army is already in place in the sewers beneath London, waiting for the signal to attack.