On a rare day off from her duties at UNIT, Liz Shaw decides to visit her friend Jean Basemore at Oakington, near Cambridge. However, Jean stands her up for their lunch, and is not to be found at her cottage: all that is there is Jean's cat and a television set — both extensively chewed. Liz telephones the Doctor, who is already on his way to Cambridge — UNIT is investigating several missing scientists. The investigation leads to the home of a cleaner, and the Doctor notices that both the cleaner and Jean had recently received reminder notices from their dentist. While the Doctor and Brigadier Lethbridge-Stewart investigate a suicide at the train station, Liz visits the dentist, Mr. Arnold. Her plans to investigate are thwarted by hypnotic music which sends her to sleep, and when she awakens, dazed and confused, she's had a new filling put in. The Doctor tells her that the dead man at the train station was the cleaner whose home they had visited earlier, and an examination of his body reveals that much of his flesh had been turned into a strange blue metal. As Liz examines the body, she notices that the flesh and bone are still transforming into the alien metal — and then she discovers that the body is full of small robots, like silverfish, which are excreting a blue liquid. One of the creatures attacks a UNIT soldier, and burrows into its flesh. Sergeant Benton attempts to shoot the creatures, but to no avail. In a last-ditch effort, Liz sprays the creatures with a fire extinguisher, which freezes them.
The Doctor identifies the creatures as Cybermats, and explains that the blue liquid is a living metal which converts human flesh into cybernetic parts — it is Cyberman technology, but the Doctor has not seen its like before. Liz's new filling is made of the same blue metal. The Doctor synthesizes an agent, based on the phosphates in the fire extinguisher, which will halt the growth of the metal. It kills the Cybermat which had burrowed into the UNIT soldier's leg, but his leg is destroyed as well. The Doctor gives Mike Yates instructions on how to create a more precise version of the agent, which will be able to be used as an antidote to revert the conversion process.
Under a mental compulsion, Liz returns to Oakington. She awakens in a buried spaceship, standing in a Cyber-conversion chamber. There, she sees her friend Jean, half-converted into a Cyberman. Jean apologizes for missing their lunch date, and begs Liz to kill her. Horrified, Liz can only watch as Jean is transformed into a Cyberman. The Doctor converses with the lead Cyberman, and realizes that the Cyberman ship had crashed on Earth years earlier, as a scout ship intended to prepare for a Cyberman invasion. Escaping with the aid of the sonic screwdriver, the Doctor and Liz discover the bridge of the Cyber-ship, where a dead, legless Cyberman is found at the helm. The Doctor realizes that the lead Cyberman was a human who had discovered the Cyber-ship and experimented with what he found there — including the blue metal. The Doctor attempts to reach the humanity in the lead Cyberman, who was once a man named Gareth Arnold. Arnold was converted by the blue metal, an experimental Cyberman technology. As the Cybermen threaten the Doctor and the blue metal in Liz's tooth begins to spread into her jaw, the Doctor uses the crude version of his antidote on the Arnold Cyberman, killing him. The other Cybermen return to their cubicles, awaiting instructions. Liz loses consciousness.
She awakens in Jean's cottage, where the Doctor completes the treatment with the advanced version of the conversion antidote. Aside from a missing tooth and some pain in her jaw, she is fine — although somewhat upset to discover that there had been a tiny Cybermat contained in the filling. But, to the Doctor's dismay, the Brigadier has converted the early, crude version of the antidote into a weapon, and uses it to destroy the remaining Cybermen.