In an attempt to adapt Medusan technology to Federation use, and vice versa, the U.S.S. Enterprise picks up Medusan ambassador Kollos, instrument specialist Laurence Marvick and telepath Dr. Miranda Jones. The Medusans have a great beauty of character, but their physical appearance causes shock to the point of insanity in humanoids.
When Dr. Jones turns down her co-worker, Lawrence Marvick's, proposal of marriage in favor of staying with Kollos, Marvick tries unsuccessfully to kill Kollos. Instead, he is driven insane by a glimpse of the Medusan. He takes over the U.S.S. Enterprise engines, which he helped design, and drives the ship out of the galaxy into an indeterminate region. The crew experiences acute sensory distortion and Marvick finally dies.
While the crew cannot pilot the starship back to the galaxy, it is possible that Kollos can, with Spock forming a mind meld. Kirk distracts Dr. Jones, who jealously objects to Spock contacting Kollos in this manner. Kirk discovers why Dr. Jones is able to gaze upon Kollos ... she's blind.
Using Spock's body, Kollos pilots the U.S.S. Enterprise back to its galaxy, but the Vulcan forgets to wear his protective visor when restoring Kollos to his box, and goes insane. Dr. Jones mind-links with Spock and draws the Vulcan's mind back to reality. She then makes a permanent mind link with Kollos and transfers with him to the Medusan vessel.