Adam Nussbaum was born in New York City on November 29, 1955 and grew up in Norwalk, Connecticut, the only child of artistic parents. He first sat at a drum kit at four, then spent five years on classical piano before getting a set of his own at around twelve. The record that marked him earliest was not a jazz record: he was five when the photographs of Huddie Ledbetter on the original Folkways ten-inch sleeves caught his eye, and the songs on those discs stayed with him for sixty years before he finally made an album out of them.

He moved to New York in 1975 to study at the Davis Center for the Performing Arts at City College, and by his own account most of his real education came from sitting in around the city rather than from coursework. He was on a record almost immediately: the pianist Peter Fish's The Silver Apple, cut at Minot Sound Studios in White Plains and issued on the tiny Ellipsoid label in 1975 with the singer Jay Clayton in the band, is the earliest commercially released session that carries his name. Work with Albert Dailey, Monty Waters, Joe Lee Wilson and Sheila Jordan followed, along with a 1977 engagement in Milwaukee alongside Sonny Rollins. Dailey's Renaissance (Catalyst, 1978) put him on record in company that included Cecil McBee, though only on two of its seven pieces, with Charlie Persip taking the rest.

Two hires in 1978 settled the shape of his career. He joined Dave Liebman's quintet, and he left school to go on the road with John Scofield, whose Rough House was recorded at Studio Zuckerfabrik in Stuttgart on November 27, 1978 with Hal Galper on piano and Stafford James on bass. What came out of the Scofield association was the trio with the electric bassist Steve Swallow that ran through the early 1980s and is still the band most often named first in any account of Nussbaum's playing. Bar Talk appeared in 1980, and two nights at the club Vielharmonie in Munich in December 1981 produced both Shinola, released in 1982, and Out Like a Light, released the following year. In the same stretch he recorded Liebman's Doin' It Again and If They Only Knew, Galper's Ivory Forest, and Ted Curson's I Heard Mingus.

The 1980s took him into larger and more varied rooms. He played with Stan Getz in 1982 and 1983, and in 1983 joined Gil Evans's Monday Night Orchestra, the loose, loud big band that held a residency at Sweet Basil in Greenwich Village; the two nights taped there on August 20 and 27, 1984 became a run of live albums, and the band took him to Europe and Japan. He worked in the George Gruntz Concert Jazz Band, with Gary Burton, with Toots Thielemans, and in the quartet Eliane Elias led with Randy Brecker. In 1987 he began touring with Michael Brecker's band. He is one of three drummers on Brecker's Grammy-winning Don't Try This at Home (Impulse!, 1988): Jack DeJohnette plays two pieces and Peter Erskine one, while Nussbaum has three, including "Chime This" and Mike Stern's "Suspone." He returned for Now You See It... (Now You Don't) in 1990, and recorded Lee Konitz's The New York Album (Soul Note, 1988) and Tom Harrell's Sail Away (1989) in the same period. In 1992 he played in the Carla Bley Big Band.

The longest of all his associations began the same year, when John Abercrombie hired him for the organ trio he was building with Dan Wall. That group made While We're Young, recorded at the Power Station in June 1992, Speak of the Devil in 1994, Tactics, taped live at Visiones in New York over three nights in July 1996, and Open Land in 1999, all for ECM, and it kept working for the better part of two decades. Nussbaum also became a fixture of the SteepleChase session economy, on dates led by Paul Bley, George Cables, Jerry Bergonzi, Vic Juris, Dave Stryker and many others.

From the mid-2000s on, much of his best work has come from bands with no single leader. The Nuttree Quartet put him with Abercrombie, Bergonzi and the organist Gary Versace for Standards (2008); a second version of the band, billed as (Another) Nuttree Quartet, swapped in Liebman and the bassist Jay Anderson for Something Sentimental. We3, with Liebman and Swallow, made Three for All (2006) and Amazing (2011). He held the drum chair in James Moody's late quartet, heard on Our Delight with Hank Jones at the piano. He was the second N in BANN, the co-operative quartet whose name spells out the initials of Seamus Blake, Jay Anderson, Oz Noy and Nussbaum, and whose single album As You Like came out on the Italian label Jazz Eyes in October 2010; the record's one Nussbaum original, "Days of Old," is co-credited to Maia Nussbaum. Alongside it ran a trio with Swallow and the saxophonist and arranger Ohad Talmor that produced Playing in Traffic (2009) and Singular Curves (2014).

The Impossible Gentlemen, formed with the English pianist Gwilym Simcock and guitarist Mike Walker and with Swallow again on bass, gave him his widest audience outside the United States. Its first album appeared on Basho in June 2011 and closes with a Nussbaum tune, "Sure Would Baby"; Internationally Recognised Aliens followed in 2013 with Steve Rodby producing, and Let's Get Deluxe in 2016 expanded the band with reeds and a string group. Then, in February 2018, at sixty-two, Nussbaum released his first album under his own name alone. The Lead Belly Project (Sunnyside) was cut in a single day at Talmor's Seeds space in Brooklyn by a quartet with no bass at all: Talmor on tenor and two electric guitarists, Steve Cardenas and Nate Radley, standing in between them for Lead Belly's twelve-string. The same band toured the material for a year and returned to Seeds on July 16, 2019 to record it again as Lead Belly Reimagined (2020).

He has remained on call. The ZZ Quartet with Ratko Zjaca, Simone Zanchini and Martin Gjakonovski, the Danish quartet US4, the New York trio A.G.N.Z. and a long run of SteepleChase dates with Stephen Riley and Jay Anderson carried him through the 2010s and 2020s, and in June 2026 ECM issued Steve Swallow's Winter Songs, recorded at Sear Sound in September 2024 with Chris Cheek, Michael Rodriguez, Steve Cardenas and Gil Goldstein, which is Swallow's first record as a leader in more than a decade and reunites a rhythm partnership that began in 1979. Nussbaum has taught as an adjunct at New York University, the New School and the State University of New York at Purchase, and gives clinics and master classes internationally.

Nussbaum is a time player first, and what musicians hire him for is a broad, elastic pulse that swings hard without ever sounding busy: the ride cymbal carries the music, the snare and bass drum comment rather than announce, and the volume stays low enough that a quartet can play a ballad at conversational level. Scott Yanow's assessment for AllMusic calls him one of the finest jazz drummers of his generation, and the range of settings is the point, because the same drummer works inside Gil Evans's electric big band, an ECM organ trio, a Danish guitar trio and a bassless folk-blues quartet without changing character. He grew up on Lead Belly's Folkways records before he ever heard bebop, and that early exposure surfaces plainly in the two Sunnyside albums, where he treats twelve-bar and one-riff material as open form rather than as a genre exercise. His partnership with Steve Swallow, which has now run from 1979 to the present, is the other formative influence: Swallow's high, singing electric bass leaves the low end open in a way that lets a drummer play melodically, and the guitar, bass and drums format of the John Scofield trio set a template Nussbaum has kept returning to, in the Nuttree Quartet, the ZZ Quartet and the Lead Belly band alike. He is also a composer with a small but persistent book of his own. "Sure Would Baby," written for his wife, has been recorded by three different bands he belongs to; "Days of Old," co-written with Maia Nussbaum, has been recorded by three more.