James Marcellus Arthur "Sunny" Murray was born September 21, 1936, in Idabel, Oklahoma, and raised in part by an uncle after his family moved to Philadelphia. He began playing drums at age nine, and as a teenager in a rough section of Philadelphia spent two years in a reformatory. In 1956 he moved to New York City, supporting himself with jobs at a car wash and as a building superintendent while working around the margins of the jazz scene with trumpeters Red Allen and Ted Curson, pianist Willie "The Lion" Smith, and saxophonists Rocky Boyd and Jackie McLean.

Everything changed in 1959, when Murray began playing with pianist Cecil Taylor. Murray later described the association as consuming, six years in which he had to invent an entirely new vocabulary for the drums; the pair spent long stretches simply practicing and experimenting, at one point attending workshops built around the music of composer Edgard Varese. In 1961 he recorded with Taylor's group on a session issued, for contractual reasons, under arranger Gil Evans's name as one side of the Impulse! album Into the Hot (1962). In 1962 Murray toured Europe for the first time with Taylor and alto saxophonist Jimmy Lyons (bassist Henry Grimes was meant to join them but fell ill), and the trio's Copenhagen engagement, later issued as Nefertiti, the Beautiful One Has Come, marked a decisive move toward fully open playing. It was also in Sweden that year that Murray and Taylor's group met tenor saxophonist Albert Ayler, who sat in with them and made an immediate impression; the expanded group recorded for Danish television, and on returning to the United States performed at Greenwich Village's Take Three club and, on December 31, 1963, at Philharmonic Hall in Lincoln Center (with Grimes back on bass) on a bill that also featured Art Blakey and John Coltrane's quintet.

Murray went on to become a working member of the free jazz circle around Archie Shepp, John Tchicai and Don Cherry known as the New York Contemporary Five, and joined Ayler's trio alongside bassist Gary Peacock. Between 1964 and 1966 he appeared on most of Ayler's essential early records, including Spirits, Ghosts, Spirits Rejoice, Spiritual Unity and Bells, and on the collective free-improvisation session New York Eye and Ear Control, which also featured Peacock, Cherry, Tchicai, Roswell Rudd and Ayler. Around 1964 Murray was reportedly offered a place in Coltrane's own band and turned it down. In 1965 he made his recorded debut as a leader with Sonny's Time Now, cut for poet LeRoi Jones's Jihad label with Ayler, Cherry, Grimes and Lewis Worrell, and featuring Jones reciting his poem "Black Art"; a self-titled quintet session followed in 1966 for ESP-Disk.

In 1968 Murray relocated to France, where he worked with Shepp and other American expatriates and recorded a run of large-ensemble leader dates for the BYG Actuel and Pathe labels, among them Big Chief (1969), Hommage to Africa and An Even Break (Never Give a Sucker) (both 1970) and Sunshine (1971), drawing on a pool of Paris-based free-jazz musicians that included Grachan Moncur III, Lester Bowie, Roscoe Mitchell, Dave Burrell and Kenneth Terroade. He later returned to the United States, settled for a time in Philadelphia, and led a group called the Untouchable Factor (Charred Earth, 1977; Apple Cores, 1978) before moving back to Europe, where he lived for the rest of his life. He reunited with Cecil Taylor for It Is in the Brewing Luminous (1981) and, decades later, for a 1996 session eventually released in 2018 as Corona. Through the 1990s and 2000s Murray recorded steadily as a leader for labels including Enja, Eremite and Foghorn, working with saxophonists Odean Pope and Sabir Mateen, pianist Aki Takase, bassist Reggie Workman, and, in the group Sound Assembly/Untouchable Factor lineages, bassist William Parker and saxophonist Charles Gayle on the 1994 trio session Kingdom Come.

A documentary, Sunny's Time Now: A Portrait of Jazz Drummer Sunny Murray, directed by Antoine Prum, was released on DVD in 2008. Sunny Murray died on December 7, 2017, in Paris, France, of multiple organ failure, at the age of 81. Archival and posthumous material has continued to surface since, including the 2019 duo session Intercommunal Dialogue 1&2 with pianist Francois Tusques and a 2026 archival release with Japanese drummer Sabu Toyozumi, Sun's Blessings, on NoBusiness Records.

Murray was among the first drummers to abandon the kit's traditional timekeeping role altogether, replacing a steady pulse with a continuous, textural wash of cymbal work, irregular snare accents and non-metronomic hi-hat patterns, often vocalizing wordlessly as he played. Critic Val Wilmer credited him with freeing the soloist from the constraints of measured time and called his unchained approach the ideal complement to Albert Ayler's own break from conventional form; writer John Litweiler went further, arguing that Murray and Ayler together did not simply bend bar lines but did away with them. Bassist Alan Silva described the effect of Murray's fast, washing cymbal technique as sounding like the end of swing itself. Alongside Cecil Taylor and Ayler, Murray helped establish the vocabulary of free jazz drumming used by generations of subsequent percussionists, and his catalog, spread across ESP-Disk, BYG Actuel, Enja, Eremite and Foghorn among many smaller labels, remains a foundational document of the music's first two decades.