Craft was born in Kingston, New York to Raymond and Arpha Craft and studied music at the Juilliard School. He became particularly interested in early music and the music of Claudio Monteverdi, Carlo Gesualdo, and Heinrich Schütz, and in contemporary music by the composers of the Second Viennese School and others.
Craft met Stravinsky in 1948, and from then until the composer's death in 1971, Craft continued to work alongside Stravinsky in a variety of roles. A relationship that started out with Craft in a rather modest role eventually evolved into a full artistic partnership. Craft compiled the libretti for Stravinsky's The Flood and A Sermon, a Narrative and a Prayer, and lived with Igor and Vera Stravinsky in Hollywood and later in New York City. Craft remained close to the composer's widow until her death in 1982.
After Stravinsky's death, Craft continued to concertize and to write. His 2002 book, An Improbable Life, details his life before, during, and after his friendship with Stravinsky. The memoir elaborates on the impact that Igor Stravinsky had on his life.
Shortly after Stravinsky’s death, Craft married the composer’s longtime nurse, Rita Christiansen, though the marriage did not endure. His survivors include a son from that marriage, Alexander; a sister, Phyllis Crawford; his second wife, the former Alva Celauro Minoff, a singer and actress; two stepchildren, Edward Minoff and Melissa Minoff; and four grandchildren.
Craft died on November 10, 2015, at his home in Gulf Stream, Florida.
Craft collaborated with Stravinsky on a series of books that covered various musical and non-musical subjects: Conversations with Igor Stravinsky (1959); Memories and Commentaries (1960); Expositions and Developments (1962); Dialogues and a Diary (1963); Themes and Episodes (1967); Retrospectives and Conclusions (1969). They include transcribed conversations between the two men, interviews culled from various published sources, essays, diary entries, and the like, all with the professed aim of presenting Stravinsky's views on music and culture.
Craft was an award-winning conductor who led most of the major orchestras in the United States (New York Philharmonic, Philadelphia Orchestra, Chicago Symphony Orchestra, Cleveland Orchestra, San Francisco Symphony, Los Angeles Philharmonic, St. Louis Symphony, and Minneapolis Symphony Orchestra), as well as international engagements in Canada, Europe, Russia, Japan, Korea, Mexico, South America, Australia, and New Zealand. He was the first American to conduct Alban Berg's Wozzeck and Lulu, and Hindemith's Cardillac. Craft also led the world premieres of Stravinsky's later, dodecaphonic works: Vom Himmel hoch, Agon, The Flood, Abraham and Isaac, Variations, Introitus, and Requiem Canticles.
Besides recording virtually all of Stravinsky's music, Craft conducted pioneering recordings of Schoenberg, Varèse, Webern and other works of then contemporary composers. While not a flamboyant conductor, Craft was known for his technically and musically precise interpretations.
He was a two-time recipient of the Grand Prix du Disque, as well as the Edison Prize for his recordings of music by Varèse and Stravinsky. His recordings of the music of Stravinsky with the Orchestra of St. Luke's were originally available on eleven now out-of-print releases from MusicMasters and seven volumes from Koch. Since early 2005, these recordings have been gradually re-released by Naxos Records.
Craft remained in a vanguard position in relation to 20th-century art music throughout his life as a conductor and musicologist. Besides working closely with one of the greats from the 20th century, Craft produced volumes of academic and personal writings on Stravinsky and on other composers.
In 2002, Robert Craft was awarded the International Prix du Disque at the Cannes Music Festival.Prejudices in Disguise (New York, 1974)
Stravinsky in Pictures and Documents (with Vera Stravinsky; New York, 1978)
Current Convictions: Views and Reviews (New York, 1977)
Present Perspectives (New York, 1984)
Stravinsky: Glimpses of a Life (New York, 1992)
Stravinsky: Chronicle of a Friendship (Nashville, 1994)
Down a Path of Wonder (Norfolk, UK, 2006)
Craft also translated and edited Stravinsky, Selected Correspondence (3 vols., New York, 1982, 1984, 1985).Craft, Robert. 2002. An Improbable Life: Memoirs. Nashville: Vanderbilt University Press. ISBN 0-8265-1381-6.
Craft, Robert. 2013. Stravinsky: Discoveries and Memories. Naxos Books. ISBN 978-1-843797-53-1