The group's origins can be traced to David Torn's album Cloud About Mercury (1987) which featured the above-listed musicians, except with Mark Isham playing trumpet. Enjoying their musical chemistry, the performers kept in touch, and formed B.L.U.E. in the mid-1990s.
The band had very unusual sound with elements of blues, rock and ambient music. Bruford and Levin were both longtime members of King Crimson, so it's unsurprising that B.L.U.E. sometimes had a "Crimsonesque" quality.