Richard Hyman was born in New York City on March 8, 1927, to Joseph C. Hyman and Lee Roven Hyman (née Rovinsky), and grew up in Mount Vernon, New York. His older brother Arthur kept a jazz record collection that introduced him to Bix Beiderbecke and Art Tatum, and his mother's brother, the concert pianist Anton Rovinsky, who gave the premiere of Charles Ives's The Celestial Railroad in 1928, gave him his classical training, including what Hyman called his sense of touch. He entered the military in June 1945, ended up in Navy band work, and then studied at Columbia University, where he won a piano competition whose prize was twelve lessons with Teddy Wilson. He married Julia in 1948.

In the late 1940s he played in Harlem, worked with the vibraphonist Red Norvo and Max Kaminsky's Dixielanders, and played at Birdland soon after the club opened in December 1949. In 1950 he toured Europe with a Benny Goodman sextet, and he went on to record with Goodman for Columbia and Capitol in 1956 and to serve as music director for Goodman's final television appearance on PBS. In the early 1950s he was the pianist when Charlie Parker and Dizzy Gillespie played "Hot House" on a New York television broadcast, one of the few surviving films of Parker playing. Most of his income came from studio work: he spent five years at NBC as pianist, organist and music director, accompanied Tony Bennett, Perry Como, Johnny Mathis, Ruth Brown and LaVern Baker, and was music director of Arthur Godfrey's television show from 1959 to 1961. He also recorded honky-tonk piano albums as Knuckles O'Toole, and other records as Willie the Rock Knox and Slugger Ryan. His own trio's 1956 version of "Moritat," the Threepenny Opera tune later known as "Mack the Knife," was a hit for MGM that is reported to have sold a million copies.

The 1960s brought his best-known detour. For Enoch Light's Command and Project 3 labels he made Lowrey organ records, among them Electrodynamics (US No. 117) and Fabulous (US No. 132), played harpsichord, and recorded as a sideman with Toots Thielemans and Wes Montgomery. In 1969 he became one of the first musicians to record on the Moog synthesizer, on Moog: The Electric Eclectics of Dick Hyman; its track "The Minotaur" reached No. 38 on the Billboard Hot 100 and is remembered as the first Moog single hit. Beck later sampled "The Moog and Me" from the same album on Odelay (1996).

From the early 1970s he turned the other way, toward the earliest jazz piano. With Hank Jones, Marian McPartland and Roland Hanna he formed the Jazz Piano Quartet, which recorded Let It Happen for RCA in June 1974. For George Wein's New York Jazz Repertory Company he organized tributes to Louis Armstrong, Duke Ellington and Jelly Roll Morton and led its tours of the Soviet Union in 1975 and France in 1977; the Armstrong concert at Carnegie Hall was issued as Satchmo Remembered (Atlantic, 1975). His Scott Joplin: The Complete Works for Piano (RCA, 1975) preceded his work on the 1977 film Scott Joplin, and Themes and Variations on "A Child Is Born" (Chiaroscuro, 1977) played Thad Jones's tune in the manner of eleven pianists, from Joplin to Cecil Taylor. In 1978 he recorded a Smithsonian collection of Morton's music, and in 1980 he led the Perfect Jazz Repertory Quintet on Say It With Music.

His long association with Woody Allen began when Allen used him as pianist on Stardust Memories (1980). Hyman went on to compose, arrange, conduct or play for more than a dozen of Allen's films, among them Zelig (1983), Broadway Danny Rose (1984), The Purple Rose of Cairo (1985), Hannah and Her Sisters, Radio Days (1987), Bullets Over Broadway (1994), Everyone Says I Love You (1996), Sweet and Lowdown (1999) and Melinda and Melinda (2004), and he was music director of The Movie Music of Woody Allen, which premiered at the Hollywood Bowl. His other scores include Moonstruck (1987). He won two Emmy Awards, one for composing and music direction on the children's program Sunshine's on the Way (1980) and one for musical direction of the PBS tribute Eubie Blake: A Century of Music (1983), and he won seven Most Valuable Player awards from the National Academy of Recording Arts and Sciences for his studio work.

He launched the Jazz in July series at the 92nd Street Y in New York with producer Hadassah Markson in the mid-1980s and was its artistic director for twenty years, stepping down in 2004, when Bill Charlap took over. He was also artistic director of the Oregon Festival of American Music. Around 1995 he and Julia moved permanently to Venice, Florida. His later records are mostly solo piano or small-group dates for Arbors Records, Reference Recordings and Victoria, including duos with Ken Peplowski (E Pluribus Duo, 2009; Live at the Kitano, 2013; Counterpoint, 2019) and with his daughter Judy, a violinist with the Horse Flies (Late Last Summer, 2012). He was inducted into the Rutgers Institute of Jazz Studies Hall of Fame and the New Jersey Jazz Society Hall of Fame in 1995, received an honorary doctorate from Wilkes University in 1996, and was named a National Endowment for the Arts Jazz Master in 2017. Julia Hyman passed away on June 16, 2025.

Hyman's reputation rests on range held under control: DownBeat described him as a pianist who can adapt to nearly any historical style, from stride to bop to modernist sound-painting. His roots are in the stride and early-swing masters he studied and recorded, Fats Waller, James P. Johnson, Eubie Blake, Zez Confrey, Jelly Roll Morton and Scott Joplin, and in Art Tatum, Teddy Wilson and Beiderbecke, alongside the classical training from his uncle and a love of Chopin's way of embellishing a melody, which he has compared to what jazz improvisers do. His scholarship shows in performance: songbook recitals devoted to Irving Berlin, Harold Arlen, Cole Porter, the Gershwins, Duke Ellington and Richard Rodgers, a lecture-recital on a century of jazz piano that became a recording, and the "Child Is Born" variations, a showpiece of style mimicry. He is equally at home as an arranger and film musician, and he has also written concertos and chamber music. The organ, Moog and studio years are a real part of his career, but the National Endowment for the Arts honored him as a jazz master, and stride, swing and ragtime piano remain the center of his reputation.