Burwell was born in New York City, the son of Natalie (née Benedict), a math teacher, and Charles Burwell, who founded Thaibok Fabrics, Ltd He graduated from King School in Stamford, Connecticut, and Harvard College, where he was a cartoonist for The Harvard Lampoon.
As a film composer, Burwell has had a long-working relationship with the Coen brothers, providing music for every film they have made (except for O Brother, Where Art Thou?, where he provided additional music to a score of traditional songs produced by T-Bone Burnett). He enjoys working with left-field directors, such as Spike Jonze. Among his best known film scores are Miller's Crossing (1990), And the Band Played On (1993), Conspiracy Theory (1997), Hamlet (2000), The Spanish Prisoner (1997), Before the Devil Knows You're Dead (2007), In Bruges (2008), Twilight (2008) Where The Wild Things Are (2009), The Blind Side (2009), and Breaking Dawn Part 1 (2011).
Burwell studied piano as a child, but eventually quit. His interest in music reignited when Steve Kraemer, a fellow high school student, taught him basic blues improvisation on the piano, which he continued with through college.
Ultimately the ethos of the punk rock movement gave him the impetus to start performing. He performed in New York with several bands, notably The Same, Thick Pigeon and Radiante.
By 1986 he had composed the music for a dance piece, RAB, which premiered at the Avignon Festival. At the same time, he was touring worldwide with The Harmonic Choir, David Hykes' experimental vocal group which specialized in overtone singing.
Burwell used the country music genre as the basis for his score for the Coens' Raising Arizona in 1987.
His work has alternated between live performance, dance and theatre commissions, and film scoring. His chamber opera "The Celestial Alphabet Event" was presented in New York in 1991 and other theatre pieces include "Mother" (1994) and "Lucia's Chapters" (2007), both with the experimental theatre group Mabou Mines.
In April 2005, Burwell composed and conducted music, performed by The Parabola Ensemble, for the plays "Sawbones" written and directed by the Coen Brothers, "Hope Leaves the Theater" written and directed by Charlie Kaufman and "Anomalisa" written and directed by Francis Fregoli. This was a segment of the sound-only production Theater of the New Ear, which debuted at St. Ann's Warehouse in Brooklyn, NY with support from Sirius Satellite Radio, United Talent Agency and Sony Pictures. It was also performed at the Royal Festival Hall in London and as part of the UCLA Live Festival in Los Angeles.
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