Originally founded in London in 1968 by a group of musicians from western England (but featuring a transatlantic lineup from 1981 onwards), the band is widely recognised as a foundational progressive rock group despite the band's own resistance to the label. The band has incorporated diverse influences and instrumentation during its history (including jazz and folk music, classical and experimental music, psychedelic rock, hard rock and heavy metal, New Wave, gamelan, electronica and drum and bass).

The band's line-up has changed many times over the years, with 18 musicians and 2 lyricists passing through the ranks. The only musician to appear in every line-up of the band has been founding guitarist Robert Fripp, although guitarist Adrian Belew was a member from 1981 to 2009 and drummer Bill Bruford from 1972 to 1997. The band is at the hub of a network of other bands and projects, and has been influential to many contemporary musical artists. The band has a large following, despite gaining little radio or music video airplay in recent years.