The story takes place on the desert planet "Plyuk" (pronounced "Plewk") in the "Kin-Dza-Dza" galaxy, where two humans - Uncle Vova and Fiddler - are accidentally stranded due to an alien teleportation device. The movie describes their long quest to find a way back home.
The natives of the planet appear human, with deceptively primitive-looking technology and a barbaric culture, which satirically resembles that of humans. They are telepathic; the only spoken words normally used in their culture are “koo” and “kew”, the latter being a swear word. The society of Plyuk is divided into two categories: Chatlanians and Patsaks. Chatlanians are privileged, and a system of rituals must be followed by the Patsaks to show flattery. The basis of their difference is unexplainable (a source of a humorous episode), and for all practical matters they are distinguished with aid of a small handheld device (visator).