Though Quine's bio cites Brazilian folk music and Gene Autry as childhood influences, he also dabbled in the blues before the Velvet Underground made a profound impact on him. Quine befriended the band and made some ragged live recordings of the Velvets; a three-CD live set from 1969 was released in 2001 as Bootleg Series, Vol. 1: The Quine Tapes. Quine would also play on Lou Reed's 1982 recording, The Blue Mask. Quine shared with Reed a love of free jazz that permeated his playing, an energetic and untethered bombardment of sound.
Quine took that sound to New York City in August 1971, where, after a brief stint in tax law publishing, he became a pivotal member of punk icon Richard Hell's Voidoids. Quine played on Hell's classic recording Blank Generation, starting a three-decade career that found him adding his immediately identifiable sound to recordings by John Zorn, Tom Waits (Rain Dogs), Matthew Sweet (Girlfriend, Altered Beast and others), Lloyd Cole, and avant garde jazz reedman John Zorn.
Last year, Rolling Stone included Quine on its list of the 100 Greatest Guitarists of All Time, calling his style "the perfect choice to complement Richard Hell's intuitive street poetry."