An alumnus in Los Angeles of Horace Tapscott's Pan Afrikan Peoples Arkestra, itself an outgrowth of the Underground Musicians' Association (UGMA), formed in 1961, Murray started out as an angry young man of jazz. While he was joining the World Saxophone Quartet, Murray recorded Flowers for Albert (june 1976) with trumpeter Olu Dara, bassist Fred Hopkins and drummer Phillip Wilson. The album contained Murray's Flowers For Albert and Ballad For A Decomposed Beauty (virtually a long solo) as well as Butch Morris' Joanne's Satin Green Dress, and introduced a visceral vibrato a` la Coleman Hawkins gone awry.

He also played on multi-instrumentalist Michael Gregory Jackson's Clarity (august 1976) that featured the stellar line-up of David Murray (tenor sax), Oliver Lake (flute, soprano sax, alto sax, talking drum) and Leo Smith (trumpet, soprano trumpet, flugelhorn, Indian flute).

The trio session of Low Class Conspiracy (june 1976), without the trumpeter, yielded more extreme sounds in Extriminity, Dewey's Circle and Low Class Conspiracy, and became the name of a band, the Low Class Conspiracy, featuring cornetist Butch Morris, pianist Don Pullen, bassist Fred Hopkins and drummer Stanley Crouch. After Solomon's Sons (january 1977), that contained solos and duets with flutist James Newton, including Murray's Theme For The Kidd and 3D Family, besides Newton's Solomon's Sons and Monk's Notice, and some solo live performances, such as Conceptual Saxophone (february 1978), Sur-real Saxophone (february 1978) and Organic Saxophone (february 1978), and several live albums such as 3D Family (september 1978), in a sax-drums-bass trio, containing colossal versions of his classics Patricia and 3D Family, a quartet with Morris recorded Interboogieology (february 1978), that contained Morris' Namthini's Shadow and Blues for David, and Murray's Interboogieology and Home, and a trio (Fred Hopkins on bass and Steve McCall on drums) recorded Sweet Lovely (december 1979), with The Hill and Hope Scope. These recordings marked a progression towards more and more sophisticated compositions. A supergroup with altoist Henry Threadgill, trumpeter Olu Dara, cornetist Butch Morris, trombonist George Lewis, pianist Anthony Davis, bassist Wilbur Morris and drummer Steve McCall crafted The Fast Life and Jasvan on Ming (july 1980), much better versions of Last Of The Hipmen and 3-D Family, besides the new Santa Barbara And Crenshaw Follies and Choctaw Blues, on Home (november 1981), and (having replaced Dara with trumpeter Bobby Bradford, and Lewis with trombonist Craig Harris, and Davis with pianist Curtis Clark) new versions of Sweet Lovely and Flowers For Albert, besides the new Murray's Steps and Sing Song, on Murray's Steps (july 1982). This was Murray's second period, when the radical style at the instrument was sidestepped to make room for the composer.

An outgrowth of the octet was David Murray's Big Band, documented on At Sweet Basil (august 1984): trumpets (Dara and Baikida Carroll), trombone (Harris), saxophones (Murray and Steve Coleman), tuba, French horn, clarinet, piano, bass, drums and Butch Morris conducting. They performed some of Murray's most exhilarating postmodernist compositions: Bechet's Bounce, Duet For Big Band, Dewey's Circle, Roses.

A new octet (with Baikida Carroll and Hugh Ragin on trumpet, John Purcell on alto) recorded New Life (october 1985), that contained Train Whistle and Blues In The Pocket. Another one (with Rasul Siddik replacing Carroll, James Spaulding replacing Purcell, Dave Burrell on piano) delivered Hope Scope (may 1987).

In parallel Murray pursued a less ambitious (but much more prolific) career as a leader of smaller ensembles devoted to simpler material and that frequently recycled old compositions and indulged in tributes to old and new masters.: Morning Song (september 1983), recorded by a quartet with pianist John Hicks, bassist Reggie Workman and drummer Ed Blackwell containing Murray's Morning Song and Off Season as well as Butch Morris' Light Blue Frolic; Children (november 1984), by a quintet with guitarist James "Blood" Ulmer and pianist Don Pullen; I Want To Talk About You (march 1986), a mediocre piano quartet with Hicks; N.Y.C 1986 (may 1986), a quartet with Ulmer, Hopkins and drummer Sunny Murray; the trio of The Hill (november 1986).

Collaborations included: Sketches of Tokyo (april 1985), with pianist Hicks, In Our Style (september 1986), with drummer Jack Dejohnette, The Healers (september 1987), with pianist Randy Weston, Daybreak (march 1989), with Dave Burrell, Golden Sea (january 1989), with Kahil El Zabar, Real Deal (november 1991), with Milford Graves, etc.

A quartet with Burrell, Hopkins and drummer Ralph Peterson recorded four albums: Deep River (january 1988), that debuted Murray's Mbizo and Theme 2A, Lovers (january 1988), Ballads (january 1988), the best of the tetralogy thanks to Murray's Ballad For The Black Man and several Burrell compositions, and Spirituals (january 1988), with Murray's Blues For My Sisters and Burrell's Abel's Blissed Out Blues. These were far more conventional works, that nodded to gospel, blues, pop and Latin music. So were The People's Choice (december 1987), by a quartet with Ragin, Hopkins and cellist Abdul Wadud, Ming's Samba (july 1988), by a quartet with Hicks, Lucky Four (september 1988), by a new quartet with Burrell, mostly composed by Burrell and bassist Wilber Morris, Special Quartet (march 1990), by a super-quartet with McCoy Tyner on piano, Fred Hopkins on bass and Elvin Jones on drums (mostly wasted on old material), Rememberances (july 1990), by a quintet with Burrell and Ragin, Shakil's Warriors (march 1991), a quartet with pianist Don Pullen and drummer Andrew Cyrille (dominated by Pullen and Cyrille compositions).

Finally Big Band (march 1991) featured three trumpets, four trombones, four saxophones, French horn, tuba, flute, piano, bass, drums conducted by Butch Morris, and contained the first significant Murray compositions in a decade: Istanbul and the 17-minute Paul Gonsalves.

The routine continued with the quintets of Black and Black (october 1991), one of the worst of his career, and Fast Life (october 1991), with Fast Life (and Branford Marsalis on tenor), the quartet of Sanctuary Within (december 1991), with the suite Sanctuary Within, the quintet with Burrell of Death of a Sideman (august 1991), the quartet with Hicks of Ballads for Bass Clarinet (october 1991).

Even the return of the Big Band, South Of The Border (may 1992), was rather disappointing. Much better was Picasso (september 1992), with the seven-movement Picasso Suite, for the octet (Ragin, Siddik, Harris, Spaulding, Burrell, Morris and drummer Tani Tabbal). These were followed by confused collections such as MX (september 1992), Body And Soul (february 1993), Saxmen (august 1993), Jazzosaurus Rex (august 1993). The more prolific Murray was, the lower the quality of his recordings. His compositional skills appeared to have completely vanished, except maybe in Fantasy Rainbow (Hicks on piano) on For Aunt Louise (september 1993). Homework (may 1994) documents a session with Bob Dickie (bass) and Robert Andreano (guitar). The Quintet (january 1994), with Ray Anderson on trombone and Anthony Davis on piano, was dominated by Davis' compositions (Andrew and Kiano). The octet of Jug-A-Lug (may 1994) introduced the synthesizer (and two guitars).

Murray contributed several of the best compositions to the World Saxophone Quartet of the 1990s: The Desegregation of Our Children on Takin' It 2 the Next Level (november 1996), the three-movement M-Bizo Suite on Mbizo (june 1999), Hurricane Floyd on Requiem for Julius (september 1999).

The live Boom Boom Cat (september 2009) featured the trio of Sunny Murray (drums), John Edwards (double bass) and Tony Bevan (soprano, tenor and bass saxes).

After the death of Julius Hemphill, the World Saxophone Quartet enrolled Kidd Jordan and James Carter for its 22nd album in 34 years, Yes We Can (2009).

The DVD Saxophone Man collects three videos.

Cherry-Sakura (april 2016) was a collaboration with pianist Aki Takase.

The Brave New World Trio, featuring bassist Brad Jones and drummer Hamid Drake, debuted with Seriana Promethea (november 2021).