From an ocean rig, a demented scientist, Krank, kidnaps children from the nearby, unnamed port city to steal their dreams, as he is incapable of having dreams of his own. Among them is the adopted little brother, Denree, of carnival strongman and former whaler One (Ron Perlman), who sets out to rescue him with the help of a little girl named Miette, a member of a thieves' guild composed entirely of orphaned children.
They delve into the world of a bio-mechanical kidnapping cult and discover the connection between the scientist and the missing Denree. Krank is both aided and hindered by his "family" - Martha, a woman with dwarfism; "uncle" Irvin, a talkative brain in a tank; and six narcoleptic, identical clones, his "brothers".
All of them were created by a bioengineering genius, who is conspicuously absent; Martha to be his wife, Irvin for intellectual company, the clones to be his brothers, and Krank to be his masterpiece. There is considerable argument amongst the clones as to who was the first one, the "Original."
They support themselves by supplying prosthetic eyes and ears to the cult which, the cult believes, give them the ability to see past an illusory world to a deeper reality. In return, the cult abducts children to be subjects for Krank's experiments. Krank is a genius but lacks the ability to dream, without which he is aging rapidly, so he uses a machine to steal children's dreams for himself.
However, he does not seem to understand that by kidnapping the children, he frightens them and causes them to have only nightmares, which are worthless to him. Conjoined twins known as the Octopus control the thieves' guild, but have become distrustful of Miette; when One accidentally bursts in and shows his strength while they are planning a heist, they hire him to help the children steal a large, heavy safe.
The safe is successfully stolen but then lost into the harbour when One is distracted by a sign of Denree's kidnappers; the Octopus then believes Miette has been holding out on them and has deserted to help One.
They employ circus performer Marcello, who was their former boss and possible captor but is now apparently in their debt, to return One to them, and much to his own distaste he allows Miette to drown while rescuing One from the cult using a system of mind control involving trained fleas, a special serum, and a music box.
Beneath the waters Miette's last sight is that of a deep sea diver who takes her to his lair beneath the harbour, and catalogues her body. He is revealed to be a delusional, paranoid amnesiac, identical to the clones except older with a beard, who hoards and lives off things that have fallen into the harbour and apparently knows something about the child abductions.
An accident revives Miette and, after taking some valuables from the stolen safe, she leaves the lair and finds One and Marcello both drowning their sorrows in a bar. Upon seeing Miette alive, the remorseful Marcello lets One leave with her.
The angered Octopus has a henchman dispose of the Marcello - though he chooses not to, resenting the Octopus' control - and uses the stolen mind control system to turn One against Miette; the smallest of actions has the largest of results in a spectacular chain of events leading to Marcello's revenge and the Octopus' demise instead, and One and Miette are freed to continue searching for Denree.
When a stolen dream escapes the rig, released by Irvin as a plea for help, it plants information in Miette's mind and restores some of the diver's memories, including how he once lived on the rig before he was attacked by Krank and Martha, and thrown into the sea. They all converge on the rig; the diver to destroy it and the duo to rescue Denree.
Miette is almost killed by the duplicitous Martha before the diver arrives and shoots the dwarf in the back with a harpoon gun. Later, Miette is forced to enter a dream world to release Denree from the dream extracting machine, whilst the deranged but vengeful diver sets a time-bomb in the rig's laboratory and then straps himself and a large amount of dynamite to the legs of the rig.
In the dream world, Miette meets Krank and makes a deal with him to replace Denree as the source of the dream; Krank fears a trap but plays along, believing himself to be in control. Miette then uses her imagination to control the dream and turn it into an infinite loop, destroying Krank's mind.
Whilst One and Miette rescue all the children, the lab is destroyed and the diver happens to grab some billowing scientific papers, finally regaining his memory of who he really is - the "Original," the genius who created the rig-dwellers in the first place.
He pleads for rescue from his remaining creations as the clones and Irvin row away in one boat, and One, Miette, and the lost children escape in another, just before a sea bird triggers the detonation of the explosives, killing the genius and destroying the rig.