The song, one of the band's bleakest, features mostly piano; the melody was something Johnny Marr had been toying around with for years, originally composed (in simpler form) as a coda to "Suffer Little Children". The song was recorded the same day as "Rubber Ring", when Marr announced that he had "a little piano thing" he wanted "to put down with Morrissey." On the original 12 inch single release, the two songs blended to become one continuous piece of music, with a vocal sample at the end of Rubber Ring merging into the howling wind heard at the beginning of Asleep. The song ends with what sounds like a music box playing "Auld Lang Syne."
It remains a fan-favourite, although it was only performed live once by the group (at Eden Court, Inverness, on 1 October 1985, the last date of the '85 Scotland tour), after a piano, which couldn't be moved, was discovered on the wings of the stage during the sound check. Morrissey was apparently in a fetal position in the center of the stage by the end of the song (Simon Goddard, The Smiths: Songs that Saved Your Life, pp. 179-182).
- Xiu Xiu performed an acoustic cover version of "Asleep" in their EP Fag Patrol.
- Carissa's Wierd performed a cover on the album Scrap Book sung by Jenn Ghetto.
- Emilie Autumn performed a cover version of "Asleep" at the Carling Islington Academy in London during her 2008 Asylum Tour.
- Death Cab for Cutie performed a rare cover of "Asleep".
- Singer and actress Emily Browning performed a cover version of "Asleep". Her cover was featured in the original soundtrack of the film "Sucker Punch", starring Browning and Vanessa Hudgens.
- There is a cover of 'Asleep' by Stars, in the album "Sing Me To Sleep: Indie Lullabies"
- In Stephen Chbosky's book The Perks of Being a Wallflower, "Asleep" is listed as being the favourite song of the main character, Charlie, and serves a major purpose in the story.
- The song "I Wish You Were Here" from Matchbook Romance's album, Voices, shares similar lyrics and themes from the song.
- Comedian and television presenter Russell Brand commented on his radio show, that he would like "Asleep" to be played at his funeral.
- Grant Morrison's run on the comic book Doom Patrol ends with the last lyrics from "Asleep": "There is another world, there is a better world... Well, there must be."
- The song was used in the Netflix comedy series "Sex Education," in a powerful scene that showed one of the main characters, Maeve Wiley, getting an abortion.