Woody Louis Armstrong Shaw Jr. was born December 24, 1944, in Laurinburg, North Carolina, and grew up in Newark, New Jersey. His father, Woody Shaw Sr., had sung in the 1930s with the gospel group the Diamond Jubilee Singers and attended North Carolina's Laurinburg Institute alongside a young Dizzy Gillespie; Shaw's mother, Rosalie Pegues, shared Cheraw, South Carolina roots with Gillespie as well. Shaw started on bugle at nine with the Newark Junior Elks drum corps, began formal classical trumpet study at eleven with Jerome Ziering, and attended Newark's Arts High School, alma mater of Sarah Vaughan and Wayne Shorter. Early on he absorbed Louis Armstrong and Harry James from records before turning to the modern language of Gillespie, Clifford Brown, Miles Davis, Kenny Dorham, Booker Little, and Lee Morgan.

By 1963, still a teenager on Newark's vibrant jazz scene alongside organist Larry Young and trombonist Grachan Moncur III, Shaw was drawing outside attention, finding work with percussionist Willie Bobo and then with alto saxophonist Eric Dolphy. At eighteen, Shaw made his recorded debut on Dolphy's Iron Man, cut at sessions arranged by producer Alan Douglas in July 1963. Dolphy invited Shaw to join him in Paris but died there in 1964 before Shaw could arrive; Shaw went anyway, spending roughly a year in Europe performing with Bud Powell, Kenny Clarke, Johnny Griffin, and saxophonist Nathan Davis, at times bringing over his Newark friends Larry Young and drummer Billy Brooks.

Back in the United States by 1964, Shaw entered a run of formative sideman work: a stint in Horace Silver's quintet (1965-1966, replacing Carmell Jones) that produced his Blue Note debut on Silver's The Cape Verdean Blues (1965), and a place on organist Larry Young's landmark Unity, recorded November 10, 1965, alongside Joe Henderson and Elvin Jones, for which Shaw composed three of the six tracks. The rest of the decade found him recording with Chick Corea, Jackie McLean, Booker Ervin, McCoy Tyner, and Andrew Hill (Grass Roots, 1968), and touring Iran with Max Roach in 1968-69.

Shaw made his first record as a leader after relocating to the San Francisco Bay Area, where he worked with vibraphonist Bobby Hutcherson and the local scene: Blackstone Legacy, recorded December 8-9, 1970 at A&R Studios in New York with Ron Carter, Lenny White, Bennie Maupin, George Cables, and Gary Bartz, and released in 1971 on Contemporary. Song of Songs followed on the same label in 1973. Back in New York by 1974, Shaw began a productive relationship with Muse Records and producer Michael Cuscuna that yielded The Moontrane (recorded December 1974), Love Dance (1976), Little Red's Fantasy (recorded June 29, 1976), and The Iron Men (recorded April 1977, released 1981), co-billed with Anthony Braxton.

Shaw signed to Columbia Records in 1977 on the strength of an endorsement from Miles Davis. Rosewood, recorded that December at CBS's 30th Street Studio with Henderson and trombonist Steve Turre, was voted Best Jazz Album of 1978 in the DownBeat Readers Poll (which also named Shaw its Best Jazz Trumpeter that year) and drew a Grammy nomination. Columbia followed with the live Stepping Stones: Live at the Village Vanguard (recorded August 1978), Woody III (recorded 1978-79 and named for his newborn son, Woody Louis Armstrong Shaw III), For Sure! (recorded December 1979), and United (recorded March 1981).

Through the 1980s Shaw kept a heavy recording schedule even as his eyesight failed to retinitis pigmentosa, an incurable degenerative condition. He cut Master of the Art and Night Music from the same February 25, 1982 Jazz Forum date with vibraphonist Hutcherson, Lotus Flower for the German label Enja, and further Muse dates including Setting Standards, Solid, and Imagination, several featuring a young Kenny Garrett on alto saxophone; Shaw also appeared as a sideman on Garrett's own 1985 Criss Cross debut, Introducing Kenny Garrett. He paired with fellow trumpeter Freddie Hubbard for two acclaimed Blue Note "trumpet summit" sessions, Double Take (recorded November 1985) and The Eternal Triangle (recorded June 1987), later combined on The Complete Freddie Hubbard and Woody Shaw Sessions. Shaw taught master classes internationally, held a faculty post alongside Henderson at Jamey Aebersold's summer jazz camps in the 1970s, and mentored younger players including Wynton Marsalis and Terence Blanchard, whose emerging acoustic post-bop movement drew heavily on his harmonic vocabulary. On February 27, 1989, by then in poor health, Shaw was struck by a subway car in Brooklyn, an accident that mangled his left arm and led to its amputation; hospitalized at Bellevue, he developed kidney failure and passed away May 10, 1989, at age 44. DownBeat inducted him into its Hall of Fame that same year.

Shaw fused the harmonic language of John Coltrane and McCoy Tyner with the trumpet lineage of Clifford Brown and Miles Davis, building a personal style around wide melodic intervals (fourths and fifths), polytonal superimpositions, and dense pentatonic runs that few other brass players of his generation attempted at speed. He had perfect pitch and, by multiple accounts, an extraordinary memory for harmony, and he studied the music of Bartok, Schoenberg, and Messiaen alongside Japanese, Indonesian, Indian, and Brazilian traditions, all of which fed a vocabulary critics and later trumpeters treated as a genuine extension of the instrument rather than a stylistic variation. Miles Davis singled him out by name as a player who could "play different from all of them," and Wynton Marsalis credited him with adding directly "to the vocabulary of the trumpet." Arriving after Coltrane's harmonic revolution and ahead of the Young Lions' return to acoustic post-bop in the 1980s, Shaw is widely regarded, including by NPR, as the last major trumpet innovator to emerge from the hard bop and post-bop tradition before that innovation curve flattened.