U2 cite the Stooges' song "1969" as the primary influence on "Desire," which is an interpolation of the Bo Diddley beat. The band originally recorded a demo of the song at STS Studios in Dublin. After re-recording it at A&M Studios in Los Angeles, they agreed it sounded "tighter and more accurate", but according to guitarist the Edge, "it lacked feel". As a result, they abandoned the re-recording in favour of the original demo.
On the Zoo TV Tour, "Desire" was re-invented with different effects on the Edge's guitar, and it opened most encores. Bono would use the song to accentuate characteristics of his onstage alteregos Mirrorball Man and MacPhisto. On the PopMart Tour, Bono and the Edge would play the song acoustically. For the Elevation Tour, it was a stripped-down electric version played at the tip of a heart-shaped walkway that extended into the audience. Adam Clayton would join in with bass just before the bridge, and Larry Mullen, Jr. played along on a single drum.
On 15 October 2004, at an appearance on British television promoting the How to Dismantle an Atomic Bomb album, Bono and Edge performed a rough electric version. On the Vertigo Tour, "Desire" was not played at all on the tour's first three legs, and appeared just once in an acoustic form on the fourth leg in response to a fan's request in São Paulo. It made a full electric debut at the beginning of the fifth leg at the second show in Sydney; this performance was ramshackle and it was refined before appearing at four subsequent concerts. "Desire" was played sporadically during the U2 360° Tour tour, usually played in a semi-acoustic form. On one occasion, it was combined with Bruce Springsteen's "She's the One." It has been played semi-regularly on the Innocence + Experience Tour during their b-stage set, often with Bono bringing someone from the crowd to play guitar with the band.
"Desire"'s B-side "Hallelujah (Here She Comes)" has never been played in full live by U2 but was debatably snippeted once during "Bullet the Blue Sky."
The music video for "Desire" was filmed in Hollywood, California and directed by Richard Lowenstein and Lynn-Maree Milburn. It is the Hollywood remix version of the song, with band members and local people in assorted places in the city, supplemented by random images pertaining to references in the song.