Their Satanic Majesties Request is the 6th British and 8th American 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 US. It is their first to be released in identical versions in both countries. The album's title is a reference to a play on the "Her Britannic Majesty requests and requires" text that appears inside a British passport.

The band experimented with a psychedelic sound on Satanic Majesties, incorporating unconventional elements such as Mellotron, sound effects, string arrangements, and African rhythms. The band 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 photographer Michael Cooper.

Satanic Majesties received mixed reactions from critics and members of the group itself. The album was criticized 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 album's release, the Rolling Stones abandoned their psychedelic style for a stripped-down return to their roots in blues music.