Hypnosis is associated with some truly remarkable phenomena. To mention just one, total anaesthesia can be induced in susceptible hypnotic subjects, so that major dental or internal surgery can be performed without any sensation of pain at all, and there’s plenty of experimental evidence, to be reviewed in the talk, that this is a genuine effect. But its interpretation is highly controversial, and the same applies to all phenomena of hypnosis and even the nature of hypnosis itself. This is the longest-running controversy in the entire history of psychology, with its origins in the 18th century when Franz Anton Mesmer was performing miraculous “cures” on members of the dissolute French nobility, and it is still deadlocked. The sceptical view, in its most extreme form, is that there is no such thing as a hypnotic trance or special hypnotic state of consciousness, and that the phenomena of hypnosis are effects of social influence. After more than two centuries of scientific research, some of the more bizarre claims that have been made for hypnosis, including its alleged usefulness in uncovering repressed memories, can be firmly rejected, but the extreme sceptical interpretation is also hard to swallow. Brain imaging is beginning to throw some new light on the nature of hypnosis, but don’t hold your breath for a resolution of the debate in this talk.