Levin was born in Brooklyn, New York, on October 13, 1947. He was a gifted pianist as a child, but at first, he focused on training as a composer, studying with Stefan Wolpe, beginning in 1957. He also took piano lessons from Louis Martin. Still a student at Andrew Jackson High School, Levin headed for France in 1960 for studies in composition with Nadia Boulanger and piano with Alice Gaultier-Léon at the Fontainebleau Conservatoire Américain. He continued to return there for further studies until 1964, with various prominent teachers. Then Levin enrolled at Harvard University, earning a magna cum laude degree with an undergraduate thesis on Mozart's unfinished works. He was immediately hired as a music theory professor at the Curtis Institute in Philadelphia, recommended for the post by pianist Rudolf Serkin, and also taught at the State University of New York at Purchase from 1970 to 1983. During the last part of that period, he also taught at the Fontainebleau Conservatoire on the recommendation of Boulanger. From 1986 to 1993, Levin taught at the Freiburg Staatliche Hochschule für Musik in Germany as well, after which he joined the faculty at Harvard. He remains there as professor emeritus.
Levin never abandoned his keyboard career, and in 1986, he made his recording debut, backing violist Kim Kashkashian on the ECM release Elegies; he has continued to champion contemporary music in addition to his Classical-period emphasis. The following year, Levin made his recital debut at Alice Tully Hall in New York. In 1994, Levin began an acclaimed series of Mozart piano concerto recordings on the fortepiano with the Academy of Ancient Music under director Christopher Hogwood; the series continued on Decca and other labels. He also recorded a cycle of Beethoven's five piano concertos on fortepiano on the Archiv Produktion label in the late '90s. Levin's recordings of Classical-period music feature innovations such as improvised cadenzas, almost undoubtedly a feature of the music in Mozart's day. By the early 2020s, he had amassed a catalog of more than 40 recordings, covering Mozart, Beethoven, Bach, contemporary music, and various kinds of chamber music. From 2007 to 2017, Levin served as the artistic director of the Sarasota Music Festival. He moved to the ECM label for a cycle of Mozart's keyboard sonatas, played on Mozart's own fortepiano, in 2022. ~ James Manheim, Rovi