Their Satanic Majesties Request is a studio album by the English rock band the Rolling Stones, released in December 1967 by Decca Records in the UK and by London Records in the United States. It was the first Rolling Stones album released in identical versions in both countries. The title is a play on the "Her Britannic Majesty requests and requires" text that appeared inside a British passport.

The band experimented with a psychedelic sound, incorporating unconventional elements such as Mellotron, sound effects, string arrangements, and African rhythms. The band members produced the album themselves as their manager/producer Andrew Loog Oldham had departed. The prolonged recording process was marked by drug use, court appearances, and jail terms by members of the band. The original LP cover features a lenticular image by the photographer Michael Cooper.

Satanic Majesties initially received mixed reviews. It was criticised as being derivative of the contemporaneous work of the Beatles, particularly their June 1967 release Sgt. Pepper's Lonely Hearts Club Band, with the similarities extending to the LP's cover. In subsequent decades, however, it has gradually risen in critical reputation. Following the release, the Rolling Stones abandoned their psychedelic style for a stripped-down return to their roots in blues music.