The band consist of Jón Þor (Jónsi) Birgisson (vocals, guitars), Kjartan (Kjarri) Sveinsson (keyboards), Orri Oáll Dýrason (drums) and Georg (Goggi) Holm (bass).  They create a remarkable sound considering the basic instruments used.  Jónsi often uses a cello bow to play his guitar, resulting in an effects-laden, atmospheric, totally unique sound.  His voice is probably the most unique thing about Sigur Rós.  A falsetto somewhere between Thom Yorke and a choir boy.  The band have released two albums so far in iceland, plus one remix album (Von brigði - recycle bin).  The first album is called Von (hope) and is quite experimental and ambient.  It often surprises people that this is a debut album, and some believe it to be a concept album but this has never been confirmed.

The band really found their feet with their second album, the masterpiece that is Ágætis byrjun (a good beginning).  The album was subsequently released in the uk in August 2000, and since then has also been released in north america through MCA records.  The band are signed to Fat Cat records in the UK and have released two singles through them, Svefn-g-englar (sleepwalkers) and Ny batterí (new batteries).  The band saw a large amount of critical acclaim throughout the world in the second half of 2000, particularly in america.  This resulted in a frantic hunt by major us labels to secure the rights to their material in america.  Large quantities of cash were offered, although in the end the band chose the deal which gave them most artistic freedom.  This was with MCA records.  The band toured north america for the first time in April and May 2001, and the vast majority of the dates sold out straight away.  Perhaps due to the hype in the american media, the shows were attended by many big name celebrities, somewhat to the band's surprise.

Sigur Rós released their third album in October 2002, entitled '( )'.  It was a darker, rawer and less accessible follow up to Ágætis Byrjun and came out to generally good reviews.  The album sold well throughout the world, and even reached #52 on the American Billboard charts.  Sigur Rós have now sold almost one million records worldwide.

The band has produced three videos, two for songs from Ágætis byrjun and one from ( ).  The band's first video, Svefn-g-englar, was released in June 2000.  The video features members of the Perlan theatre group, an Icelandic group of downs syndrome actors who regularly perform in Iceland.  The second video, for Viðrar vel til loftárása, was released in September 2001.  This remarkable video is set in the 1950's and follows the story of two young boys.  The end of the video features a football match involving the boys, with a surprising and monumental climax.  The band's third video, 'untitled 1' (aka vaka), was directed by the highly respected Italian director and photographer Floria Sigismondi, and was released in February 2003. the video was a considerably dark affair, featuring playing children in a post-apocalyptic playground covered in black snow, where they must play under the protective guise of gasmasks.

Earlier this year, Sigur Ros began an extensive european tour, including a sold out show at the 4,000 capacity hammersmith Apollo Theatre in London.  In march they toured the United states where they played at some of the biggest headline shows, including a concert at the 6,000 capacity Radio City Music hall in New York.