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Space exploration was big at the time, and was probably an influence on this. Pink Floyd was making music with a similar sound.
The psychedelic sound reflected the times. It was the summer of love (1967).
Mick Jagger got the idea for this while in jail on drug charges.
The Stones played this on their Steel Wheels tour in 1989. A show in Atlantic City was broadcast with this song shot in 3D, which viewers could see using those goofy glasses.
Various echo effects and drum sounds were added in overdubbing.
Brian Jones played the Mellotron, an early synthesizer. He died in 1969 when he drowned in his swimming pool.
'90s Psychedelic group The Brian Jonestown Massacre recorded a tribute to the Stones' Psychedelic period (and this song) called Their Satanic Majesties' Second Request. (thanks, Bertrand - Paris, France)
The man who created Yacht Rock with "Sailing" wrote one of his biggest hits while on acid.
Did Eric Clapton really steal George's wife? What's the George Harrison-Monty Python connection? Set the record straight with our Fact or Fiction quiz.
Joshua Scott Jones explains why he's always asking forgiveness from his musical partner, who's also his girlfriend.
The good doctor shares some candid insights on recording with Phil Spector and The Black Keys.