"Relax" is the debut single by English new wave band Frankie Goes to Hollywood, released in the United Kingdom by ZTT Records in 1983. Produced by Trevor Horn and featuring the band along with other musicians, entered the UK Top 75 singles chart in November 1983 but did not crack the Top 40 until early January 1984. Three weeks later it reached number one, on the chart dated 28 January 1984, replacing Paul McCartney's "Pipes of Peace". One of the decade's most controversial and most commercially successful records, "Relax" eventually sold a reported two million copies in the UK alone, easily ranking among the ten biggest-selling singles in the UK. It remained in the UK Top 40 for 37 consecutive weeks, 35 of which overlapped with a radio airplay ban by the BBC (owing to lyrics perceived as overtly sexual).

In June 1984, bolstered by the instant massive success of the band's follow-up single "Two Tribes", the single re-entered the Top Ten for a further nine weeks, including two spent at no. 2 (behind "Two Tribes"). At that time, Frankie Goes to Hollywood were the only act apart from the Beatles and John Lennon to concurrently occupy the top two positions on the chart. Several 12-inch single versions (and the "Frankie Say Relax" T-shirt craze) further fed the "Relax" phenomenon. The single re-entered the UK Top 75 in February 1985 and, more successfully, in October 1993, when it spent three weeks in the Top Ten. "Relax" remains the UK's biggest-selling debut single of all time.

In the United States "Relax" was also comparatively slow in reaching its chart peak. Released in March 1984, albeit with a different mix and nearly a minute shorter in length, the single stalled at no. 67 on Billboard's Hot 100 in May during a seven-week run, but it ranked number one for the year on the Los Angeles "alternative rock" station KROQ, as voted for by listeners. In January 1985, a release of "Relax" that was far more similar to the UK hit version entered the Hot 100 at no. 70, and in March it reached no. 10 during its 16-week run. In January 1989, the single was certified gold by the RIAA.

In February 1985, the record was awarded Best British Single of 1984 at the Brit Awards, and Frankie Goes to Hollywood won Best British Newcomer. A version of the song features on Frankie Goes to Hollywood's debut album Welcome to the Pleasuredome, released in October 1984.

Frankie Goes to Hollywood formed in Liverpool in 1980. The singer, Holly Johnson, said he wrote "Relax" in his head, and that the lyrics came to him as he was walking down Princess Avenue in Liverpool. In February 1983, the band performed an early version of "Relax" on the Channel 4 show The Tube, dressed in fetish wear. This version included a bridge that incorporated lyrics from the song In Heaven from David Lynch's film Eraserhead.

That May, Frankie Goes to Hollywood became the first act signed by ZTT Records, a new record label co-founded by the producer Trevor Horn, who saw their Tube performance. "Relax" was selected as their first single. Horn described the original version as "more a jingle than a song", but he preferred to work with songs that were not professionally finished because he could rework them in his own style.

Horn dominated the recording of "Relax" in his effort for perfectionism. Initial sessions were held at the Manor Studio. The band were overawed and intimidated by Horn's reputation, and were too nervous to make suggestions. Johnson said in his autobiography, "Whatever he said we went along with".

According to Horn, the "Relax" demo featured the guitarist Jed O'Toole, the brother of the bassist, Mark O'Toole. By the time Frankie Goes to Hollywood signed to ZZT, Jed had been replaced by Brian Nash. Though he acknowledged that Nash later became a good guitarist, he felt he was not skilled enough, and wanted to try the song with other musicians. Horn recorded a version with the former Ian Dury backing band the Blockheads, with Norman Watt-Roy on bass. The sessions were deemed to be not modern-sounding enough. Instead, Horn replaced Watt-Roy's with a sampled E note on a bass guitar, which was layered over a Linn 2 bass drum.