The group consists of rappers Hössi Ólafsson (later replaced by Egill Olafur Thorarensen), Ómar Örn Hauksson, Steinar Orri Fjeldsted, and Sölvi Blöndal (who also acted as producer, keyboardist, percussionist, drummer and songwriter).
On 31 August 2000, Quarashi announced that they had signed with Sony Music Entertainment Incorporated under the Columbia Records label.
The deal was to last for six albums, the first of which would be produced in collaboration with Cypress Hill DJ, DJ Muggs, and Brendan O'Brien, who was the recording director for the Red Hot Chili Peppers breakthrough hit album, Blood Sugar Sex Magik, and helped produced three of Rage Against the Machine's hit albums, Evil Empire, The Battle of Los Angeles, and Renegades.
After the recording of the album, Sölvi Blöndal and Hössi Ólafsson produced the soundtrack for the Halldór Laxness play, Kristnihald undir Jökli, which was directed by Bergur Þór Ingólfsson, and ran in the Borgarleikhús in the winter of 2001.
"Stick 'Em Up" was nominated for a 2002 MTV Video Music Award for Best Art Direction (which they lost to Coldplay's "Trouble").
Quarashi produced "Mess It Up" in July 2003, a song which featured Steini trading verses with underground Icelandic rapper Opee (real name Ólafur Páll).
Opee did one more song with Quarashi, "Orð Morð" featuring Icelandic musician Jóhann G. Jóhannsson.
Quarashi started an on-line blog in December 2003, to discuss the recording process and to announce upcoming dates.
Quarashi also performed during a long weekend in Iceland called "The Verslunarmanna Helgi", where they played gigs at Sauðárkrókur and Akureyri.
On 24 February 2004, Columbia Records announced that they had dropped Quarashi from the label due to the disappointing sales of Jinx.
On 14 October 2004, Quarashi released Guerilla Disco in Iceland under the Skífan and Dennis Records labels.
Also in October 2004, Quarashi teamed up with the stars of the popular Popptíví (the MTV of Iceland) TV show, 70 Minutes, to make a song and music video called "Crazy Bastard".
The song and video became a fan favourite, and when more copies of Guerilla Disco were made, "Crazy Bastard" was added as a bonus track on the CD.
In May 2016, during an interview on Icelandic television station RÚV, Sölvi and Steini confirmed that a new album was in the works that would include all five original members.
According to the comments made by the band on the announcement, the box set contains previously unreleased material.
The box set includes double colored vinyl, CD, and cassette versions of the collection, along with stickers, key chains, tote bag, and a finger skateboard (finger-board).
Hössi Ólafsson founded the group with Sölvi and Steini in 1996, and served as the lead vocalist and frontman, but left in 2002.