By 1992 The Sugarcubes dissolved as different members of the band had realised they all had different ambitions; Instead of risking their friendship, the band went on an indefinite hiatus. They remain friends to this day and are all still involved in the management of Smekkleysa/Bad Taste. Björk moved to London and began thinking about a solo career; to this end, she began working with producer Nellee Hooper, who had produced for Massive Attack, among others. Their partnership produced Björk's first international solo hit, "Human Behaviour". Her solo debut album, simply titled Debut, was released in June of 1993 to positive reviews; it was named album of the year by NME, and eventually went platinum in the United States. At the 1994 Brit Awards Björk won the awards for Best International Female and Best International newcomer. * Debut was a mix of songs Björk had written since she was a teenager as well as newer lyrical collaborations with Hooper.

The success of Debut enabled her to collaborate with other artists on one-off tracks. She worked with David Arnold on "Play Dead", the theme to the 1993 film The Young Americans (which appeared as a bonus track on a re-release of Debut), collaborated on two songs for Tricky's Nearly God project, appeared on a track on the 1997 album Not For Threes by Plaid, which was released on the cult Warp Records label, and wrote the song "Bedtime Story" for Madonna's 1994 album Bedtime Stories.

Björk returned to the studio during 1994 to work on her next solo album with Nellee Hooper, Tricky, Graham Massey of 808 State, and electronic music producer Howie B. The album, Post, contained songs based on Björk's relationships and songs about love (one of her favorite subjects), as well as some angry and confrontational material. Like "Debut," it was a collection partly made up of songs she had written in past years.

She wrote the song "Bedtime Story" for Madonna's 1994 album Bedtime Stories (parts of which Björk reused in her own song "Sweet Intuition", released as a b-side on the 'Army Of Me' single) and performed on MTV Unplugged during this time. By 1995, the new album Post was ready; it was released in June, reaching number two on the UK's album charts, and also went platinum in the United States. The album was boosted further by the success of the single It's Oh So Quiet, a surprise christmas hit which sold 400 000 copies in the United Kingdom and spent 15 weeks on the chart. * January of 1997 saw the release of Telegram, an album of uncharacteristic previously-released remixes of songs from Post and a non-LP song "My Spine".

2004 saw the release of Björk's Medúlla, in late August. Medúlla had been more of an impromptu piece of work after the two concept albums, but in the midst of production Björk decided the album would work best as an entirely vocal-based album. The majority of the sounds on the album are created by vocalists (although these sounds are often electronically distorted). Björk used the vocal skills of throat-singer Tagaq, hip hop beatboxer Rahzel, Japanese beatboxer Dokaka, avant-rocker Mike Patton, Soft Machine drummer/singer Robert Wyatt, and several choirs; she again appropriated text from poet E. E. Cummings for the song "Sonnets/Unrealities XI." Medúlla has a raw, guttural, and ancestral feel. Medúlla became her highest ever charting album in the USA, debuting at number 14.

In August 2004 Björk performed the song "Oceania" (from her Medúlla album) at the Opening Ceremony of the 2004 Summer Olympics in Athens, Greece. In typical Björk style, her performance was one of the more unusual ones of the event. As she sang, her dress slowly unravelled to reveal a 10,000 square foot (900 m²) map of the world, which she let flow over all of the Olympic athletes. The song "Oceania" was written especially for the occasion and features the vocals of Shlomo, a Leeds based beatboxer, and a London choir. An alternate version of the song began circulating on the internet with additional vocals by Kelis. Though some were confused as to the authenticity of this collaboration, Björk's camp confirmed its legitimacy. It originally appeared on the promotional "Oceania" single released to radio stations and later became available to the public as a b-side of the "Who Is It" single, which charted at number twenty-six in the UK. This was followed in early 2005 by "Triumph of a Heart," charting at number thirty-one. A video for the potential next single, "Where Is the Line?", was filmed in collaboration with the Icelandic artist Gabríela Fridriksdóttir in late 2004, and was released exclusively on the "Medúlla Videos" DVD.

Other than these few performances, no concerts or tours were arranged to promote Medúlla. Björk said in numerous interviews that this was because she wished to immediately continue writing and recording yet another new album. She spoke to Rolling Stone in June 2004: "Every album I've done, the minute that it's done, I feel really lubricated and, like, 'Wow, now I can write an album in five minutes'... And I just want to find out if that's just a fantasy or if it's true." *

After the disastrous tsunami which struck Southeast Asia in late 2004, Björk began work on a new project, Army of Mixes. This project recruited fans and musicians from around the world to either cover or remix the 1995 track, "Army of Me". From over 600 responses, Björk and her co-writer Graham Massey, picked the best twenty to appear on the album. The album was released in April in the UK and in late May 2005 the US. It peaked at number fourteen on the dance albums chart in the UK. * By January 2006, the album had raised around £250,000 to help UNICEF's work in the south east Asian region. * Björk visited Banda Aceh in February 2006 to view some of UNICEF's work with the children who were affected by the tsunami. *

Björk's intermittent acting career began in 1990, when she appeared in The Juniper Tree, a tale of witchcraft based on the Brothers Grimm story of the same name. Björk played the role of Margit, a girl whose mother has been killed for practicing witchcraft. Björk also had an uncredited role in 1994's Prêt-à-Porter.

Björk also prominently appeared in the documentary Screaming Masterpiece (2005). The film delves into the intense and diverse Icelandic music scene. The movie features archive footage of The Sugarcubes and Tappi Tíkarrass, and an ongoing conversation with Björk herself.

In 1999, Björk was asked to write and produce the musical score for the film Dancer in the Dark, a genre-bending musical via drama about an immigrant named Selma who is struggling to pay for an operation to prevent her son from going blind. Director Lars von Trier eventually asked her to consider playing the role of Selma, a proposal she initially turned down. He then threatened to stop the project, which would have made all the musical work she had already done useless. Eventually, she accepted. Filming began in early 1999, and the film debuted in 2000 at the 53rd Cannes Film Festival. Björk received the best actress award for her role, and yet she described the shoot as so physically and emotionally trying that she has sworn off acting ever again. This was a rumour, however that was put to rest in numerous interviews. Björk later stated that she always wanted to do one musical in her life, and this was the one. She also said that she could not do movies and music at the same time. The soundtrack Björk created for the film was released with the title Selmasongs. The album features a duet with Thom Yorke of Radiohead titled "I've Seen it All". She was invited to record Gollum's Song for the film The Lord of the Rings: The Two Towers, but declined the invitation, as she was then pregnant; the track was instead recorded by her fellow Icelander Emilíana Torrini.

Her New York-based long-time boyfriend Matthew Barney is a major contemporary artist. Björk collaborated with him on the experimental art film Drawing Restraint 9, a dialogueless exploration of Japanese culture. Björk and Matthew both appear in the film. She says that what she does in the film isn't acting; it's being a human sculpture. She is also responsible for the film's soundtrack, her second after 2000's Selmasongs.

Björk usually goes by her first name only. This is not a stage name or affectation; it is normal for an Icelander to be referred to by his or her first name, as the last name simply indicates the name of the father (or occasionally the mother). See Icelandic naming conventions.

Björk means "a birch tree" in Icelandic (the meaning of Icelandic names is often transparent), cognate with Old English beorc and the modern English word. Though many English-speakers pronounce her name "Byork", a more accurate approximation would be "Byirk", which she has pointed out rhymes with "jerk". * Guðmundsdóttir is pronounced roughly "GVUTH-muns-doh-tear", and means "Guðmundur's daughter".

Björk's father, Guðmundur Gunnarsson, is a well known union leader in Iceland and was nationally recognized before his daughter became famous. Her mother's name is Hildur Rúna Hauksdóttir.