In the distant future, the gargantuan blue humanoid Draags have brought human beings (who are called Oms as a play on the French word for "man", homme) from Earth to the planet Ygam, where they maintain a technologically and spiritually advanced society. The Draags consider Oms animals, and while they keep some as pets, others live in the wilderness and are periodically slaughtered by the Draags, who wish to control their population. Draags have much longer lifespans than Oms, but reproduce much less.
When an Om mother is teased to death by three Draag children, her orphaned infant is found by Master Sinh, a key Draag leader, and his daughter Tiva, who keeps the boy as a pet and names him Terr. Tiva loves Terr and is careful not to hurt him, but, in accordance with her parents' instructions, keeps him under control, giving him a collar with which she can pull him in any direction. She brings Terr to sessions in which she receives her education using headphones that transmit knowledge into her mind, and a defect in his collar allows him to receive the knowledge too. Around the time that Tiva grows into her teens and first performs Draag meditation, which allows the species to travel with their minds, she loses some interest in Terr, who has become a young man and acquired much Draag knowledge. He escapes into the wilderness, stealing Tiva's headphones.
There he runs into a wild female Om, who cuts off his collar and introduces him to her tribe, which lives in an abandoned Draag park full of strange creatures and landscapes. Terr shows them how to use the headphones to acquire Draag knowledge and literacy, winning the right to do so in a duel. The literacy they gain allows them to read a Draag announcement that the park will be purged of Oms, and, when the purge comes, some are slaughtered by Draag technology while others escape, joining forces with another tribe. They are attacked by two Draag passers-by and manage to kill one of them before escaping to an abandoned Draag rocket depot, much to the outrage of Draag leaders. They live there for years, joined by many other Oms, and, due to the knowledge acquired from Terr's headphones, manage to replicate Draag technology, including two rockets; they hope to leave Ygam for its moon, the Fantastic Planet, and live there safe from Draags. When a large-scale Draag purge hits the depot and many Oms are slaughtered, a group led by Terr uses the rockets to flee to the Fantastic Planet, where they discover large statues that Draags travel to during meditation and use to meet beings from other galaxies in a strange ritual that maintains their species. The Oms destroy some of the statues, threatening the Draags' existence; the genocide is halted on Ygam, and, facing a crisis, the Draags sue for peace. This leads to an era of peaceful coexistence between the two species, who now benefit from each other's way of thinking.
