In a surreal, dystopian society, an aging mad scientist named Krank experiences an inability to dream, which has halted his aging process and is causing him to grow prematurely old. Desperate to reverse this curse, Krank has been abducting children from a local port town to steal their dreams. He is aided by a cult of cyclops, a brain in a tank named Irvin, a pair of conjoined twins, and a host of other grotesque characters, all of whom share the floating oil rig where Krank carries out his nefarious experiments.

Among the town's denizens is a strongman named One, who forms an unlikely bond with a cunning orphan girl named Miette. After his adopted little brother is kidnapped by Krank's minions, One sets out on a mission to rescue him. The pair traverse the dark, atmospheric world filled with bizarre encounters and challenges. Along their journey, they uncover the depths of Krank's madness and the sad history that led him to his current state, while forming a close connection that changes them both.