Greg Murphy is a Chicago native who has worked the New York jazz scene since the late 1980s. He started young: he joined the Ray-Fisk Grammar School Band in 1971 and began classical piano study that same year with Lucia Santini at Roosevelt University. As a teenager and young adult in Chicago he passed through Lightning Flash Thunder Roar and the big bands at the University of Illinois at Chicago and Northern Illinois University. In 1984 a jazz study grant from the National Endowment for the Arts took him to New Orleans to study with pianist and educator Ellis Marsalis. He stayed on to work the local scene with the New Orleans Jazz Couriers and Percussion Incorporated and to lead his own group, the Fusicians; by his own account his first recording credit came in 1987, on a session called Drum Talk.

Murphy relocated to New York City in 1987 and, in the same year, began a working relationship with drummer Rashied Ali, John Coltrane's last drummer, that ran for twenty-two years, until Ali's death in 2009. Murphy joined Ali's downtown repertory band Prima Materia as its pianist after the group's original bassist, William Parker, left; the quintet that resulted, with Murphy at the piano opposite the remaining bassist Joe Gallant, is the lineup most listeners mean by the group's name. Murphy is on both of Prima Materia's mid-1990s studio-quality live albums, cut at the Knitting Factory: Meditations (recorded June 23, 1995), a reading of Coltrane's 1965 suite, and Bells (recorded May 17, 1996), a single unbroken performance of Albert Ayler's 1965 piece, with saxophonist Allan Chase transcribing the Ayler material from the original recording. The band toured Europe with Murphy in 1995, including a full concert at Burghausen, Germany, that March. When Murphy was unavailable, Uri Caine sat in on piano; later in the group's run, bassist Wilber Morris shared the bass chair with Gallant, and it is that pairing, with Murphy still at the piano, that appears on the group's excerpt of "Meditations" on AUM Fidelity's Vision Volume One: Vision Festival 1997 Compiled and, years later, on both bassists together on Prima Materia's final release, Configurations (The Music of John Coltrane), dated to the day of Ali's death, August 12, 2009.

Murphy's other major thread with Ali ran through Ali's own working quintets. In June 1992 he was part of the session that became No One in Particular, not released until 2001, reuniting Ali with Ravi Coltrane and Matthew Garrison, the sons of John Coltrane and Jimmy Garrison, alongside guitarist Gene Ess, billed on that release under his birth name, Gene Shimosato. Discogs credits Murphy on that release as "Drums," alongside Ali, which is almost certainly a data-entry error carried over from the same session credits Rashied Ali's own JazzProfiles.com profile flags for the same reason: there is no piano credit anywhere on the release, Ali is its only drummer, and Murphy is documented elsewhere, including on his own website, as the group's pianist. In the 2000s Murphy played piano in a reconstituted Rashied Ali Quintet alongside bassist Joris Teepe, tenor saxophonist Lawrence Clark, and trumpeter Jumaane Smith, recording both volumes of Judgment Day on February 17 and 18, 2005 (issued 2006). A later edition of the same quintet, with trumpeter Josh Evans in Smith's chair, cut Live in Europe at the Jazz Happening festival in Tampere, Finland, on November 2, 2007, released in 2009, the year of Ali's passing. A third, earlier trio document, In France, recorded in Roanne in March 1989 with bassist Tyler Mitchell and saxophonist Antoine Roney, was also issued posthumously in 2009.

Alongside the Ali association, Murphy built a leader catalog of his own. He launched it on his own Murphasaurus Records imprint with Let's Get Started, recorded at Night Owl Studios in New York in April 1994 but not released until 2004, and followed it with Orientation (2006), a quintet date with saxophonist Lawrence Clark and percussionist Raphael Cruz. He moved to the New England-based Whaling City Sound and Jazzintensity labels for the bulk of his later leader work: Blues for Miles (2014), which included the piece "Brother, Can You Spare a Dime?," later used in the HBO documentary Redemption that earned an Academy Award nomination in 2013; Summer Breeze (2016), a larger session with trumpeter Josh Evans; the trio album Bright Idea (2019), with drummer Jeff "Tain" Watts and bassist Eric Wheeler, which topped the JazzWeek jazz chart; Cool Water (2021), the same trio expanded with guests including vibraphonist Bill Ware, trombonist Frank Lacy, and keyboardist David Kikoski; You Remind Me (2024); and Snap Happy (2025), his eighth album as a leader, again reaching number one on JazzWeek and featuring guitarist Mark Whitfield and vocalist Sy Smith. Along the way he has toured France, Ireland, Japan, China, and the Philippines, and has performed alongside Ornette Coleman, Carlos Santana, and Archie Shepp.

Murphy's musical identity splits cleanly along the two halves of his career. The Rashied Ali association put him inside the most demanding repertoire in the free-jazz canon, Coltrane's and Ayler's late, harmonically open compositions, played at full length with Ali's "multi-directional" drumming as the engine underneath. AllMusic's Chris Kelsey, writing on Prima Materia, credited Murphy's "percussive attack" with raising the group's intensity once piano replaced the band's original two-bass frontline. On his own records, by contrast, Murphy works a more conventional but still wide-ranging book of standards, blues, and originals, described by All About Jazz's Jack Bowers as pairing "superb technique" with "sharp and creative digressions," and by Jazzwise as showing "impressive skills both on keyboard and as composer." Reviewers of his later Whaling City Sound albums have repeatedly noted the same range inside a single record: straight-ahead swing sitting next to fusion grooves and freer, open playing, a combination that traces directly back to a pianist equally at home accompanying Ali's most abstract music and leading a mainstream piano trio.