The Rocky Horror Show is a musical with music, lyrics and book by Richard O'Brien. A humorous tribute to various B movies associated with the science fiction and horror genres from the 1930s to the early 1960s, the musical tells the story of a newly engaged couple getting caught in a storm and coming to the home of a mad transvestite scientist, Dr Frank-N-Furter, unveiling his new creation, Rocky, a sort of Frankenstein-style monster in the form of an artificially made, fully grown, physically perfect muscle man.

The show was produced and directed by Jim Sharman. The original London production of the musical was premiered at the Royal Court Theatre (Upstairs) on 19 June 1973 (after two previews on 16 and 18 June 1973). It later moved to several other locations in London and closed on 13 September 1980. The show ran for a total of 2,960 performances in London and won the 1973 Evening Standard Theatre Award for Best Musical. Songs in the musical include "Time Warp" and "Sweet Transvestite" (co-written by O'Brien and Richard Hartley), while the costumes were designed by Sue Blane. Its 1974 debut in the US in Los Angeles had a successful nine-month run, but its 1975 Broadway debut at the Belasco Theatre lasted only three previews and forty-five showings, despite earning one Tony nomination and three Drama Desk nominations. Various international productions have since spanned across six continents as well as West End and Broadway revivals and eight UK tours. In 1991 it was nominated for the Laurence Olivier Award for Best Musical Revival. Actor Tim Curry, who originated the role of Dr. Frank-N-Furter, became particularly associated with the musical.

The musical was adapted into the 1975 film The Rocky Horror Picture Show, starring O'Brien as Riff Raff, with Curry also reprising his role; the film has the longest-running release in film history. In 2016, it was adapted into the television film The Rocky Horror Picture Show: Let's Do the Time Warp Again. The musical was ranked eighth in a BBC Radio 2 listener poll of the "Nation's Number One Essential Musicals", and it was one of eight British musicals featured on a commemorative stamp issued by the Royal Mail in 2011.

Beyond its cult status, The Rocky Horror Show is also widely said to have been an influence on countercultural and sexual liberation movements that followed on from the 1960s. It was one of the first popular musicals to depict fluid sexuality during a time of division between generations and a lack of sexual difference acceptance. Like the film adaptation, the musical is noted for a long-running tradition of audience participation through call-back lines and attending dressed up as characters from the show. On the 50th anniversary of the musical in 2023, BBC News states that since debuting in London in 1973 the "production has been performed in 20 different languages" and been "seen by 30 million people globally".

As an out-of-work actor in London in the early 1970s, Richard O'Brien wrote The Rocky Horror Show to keep himself busy on winter evenings. Since his youth, he had developed a passion for science fiction and B horror movies; he wanted to combine elements of the unintentional humour of B horror movies, portentous dialogue of schlock-horror, Steve Reeves muscle films, and fifties rock and roll into The Rocky Horror Show. A major theme running throughout the musical is transvestism, which according to O'Brien was not originally meant to be as prominent as it ended up being. He conceived and wrote the play set against the backdrop of the glam era that had manifested itself throughout British popular culture in the early 1970s; he has stated "glam rock allowed me to be myself more", allowing his concept to come into being.

O'Brien took a small portion of his unfinished Rocky Horror to Australian director Jim Sharman, who decided he wanted to direct it at the small experimental space Upstairs at the Royal Court Theatre in Sloane Square, Chelsea, London, which was used as a project space for new work. Sharman had received considerable local acclaim as the director of the original Australian productions of Hair and Jesus Christ Superstar. He went to London to direct the first British stage production of Superstar, during which he met O'Brien, who had played King Herod for just one performance. Sharman brought fellow Australians Nell Campbell and long-time scenic designer partner Brian Thomson into the production.

Star Tim Curry recalled his first encounter with the script:

I'd heard about the play because I lived on Paddington Street, off Baker Street, and there was an old gym a few doors away. I saw Richard O'Brien in the street, and he said he'd just been to the gym to see if he could find a muscleman who could sing. I said, "Why do you need him to sing?" [laughs] And he told me that his musical was going to be done, and I should talk to Jim Sharman. He gave me the script, and I thought, "Boy, if this works, it's going to be a smash."