The Doctor and his companions Ben and Polly arrive in the TARDIS at the South Pole in the year 1986, near the Snowcap base. The base is supervising the mission of the Zeus IV spaceship, running a routine probe on the Earth's atmosphere.
Unusual readings on the spaceship's instruments lead to the discovery of a new planet suddenly approaching Earth. The spaceship begins to experience power losses, and Snowcap personnel begin arrangements to abort its mission.
Back on the base, the Doctor reveals what he knows about the tenth planet: it is Mondas, Earth's former sister planet, and its inhabitants will soon be visiting Earth. True to his prediction, three robotic creatures land outside, killing the guards and disguising themselves in the dead men's furs to gain access.
While everyone is distracted by their efforts to land Zeus IV safely, the creatures are easily able to take over the base. The base personnel and Polly plead with the invaders to allow them to save the lives of the Zeus IV crew, but the creatures say that their lives are irrelevant to them. They explain that they are Cybermen, who were once like human beings, but gradually replaced their bodies with mechanical parts, including eliminating the "weakness" of emotion from their brains. The Cybermen allow the men to make contact with Zeus IV, but it is too late as the ship is dragged away by Mondas and explodes.
The Cybermen explain that Mondas is absorbing energy from Earth and will soon destroy it. They propose to take humans back to Mondas and turn them into Cybermen.
Ben, who has been imprisoned in the projection room after attempting to kill a Cyberman, rigs up the projector to blind incoming Cybermen, allowing him to steal his guard's weapon and kill him. Sneaking back into the Tracking Room, he hands the cyberweapon to General Cutler, the base commander, who kills the remaining two Cybermen. Cutler contacts Space Command HQ in Geneva and is informed that they have sent his son on a mission to rescue the doomed Zeus IV.
Cutler decides it is time to take the fight to the Cybermen and decides to use the powerful Z-bomb to destroy Mondas. Ben argues against using the bomb, saying that Mondas might destroy itself anyway when it absorbs too much energy. The chief scientist at Snowcap, Dr. Barclay, is also concerned, saying that the radiation caused by the exploding planet would cause great loss of life on Earth. Unswayed, Cutler orders Ben to be imprisoned in a cabin with the Doctor, who is unconscious and seemingly ill.
Barclay goes to Ben and tells him how to sabotage the rocket to prevent it from reaching Mondas, but Cutler notices Barclay's absence and catches Ben in the act. Cutler attempts to fire the Z-bomb, but the engines fail on the launchpad thanks to Ben's sabotage. Cutler, enraged, threatens to kill Ben, Barclay, and the Doctor, who has now regained consciousness. Before he can shoot the Doctor, Cutler is killed by the leader of a newly arrived squad of Cybermen.
The Cybermen insist that the rocket pointed at Mondas be dismantled. The Doctor suggests that it would be a good idea to go along with this, and tells the others to play for time, as Mondas cannot take much more energy now. The Cybermen take Polly back to their spaceship as a hostage.
As the Cybermen take over the world, the Doctor realises that their plan is to destroy the Earth with the Z-bombs, thus saving Mondas. He manages to communicate this revelation to Ben and the others over the intercom before the Cybermen take him prisoner. In the radiation room, Ben surmises that the reason why they need to use humans to do this work rather than doing it themselves is that they are highly susceptible to radiation. Barclay suggests using the rods from the reactor chamber as a portable weapon against the Cybermen. This proves successful, allowing Ben, Barclay, and the others to regain control of the base. More Cybermen enter the Tracking Room, but just at that moment Mondas explodes, disabling all the remaining Cybermen.
Cutler's son contacts the base from Zeus V, telling them that his ship is now back to full power, and Geneva tells Barclay that the Cyberman threat has ended all over the world.
Meanwhile, Ben has made his way back to the Cybermen's ship to rescue the Doctor and Polly. The Doctor appears to be very ill and confused and makes his way back to the TARDIS. Inside the TARDIS, the Doctor falls to the floor, and before the astonished eyes of his companions, his cells renew themselves for the very first time, and he transforms into a younger man.