Artie Shaw was born Arthur Jacob Arshawsky on May 23, 1910, in New York City, the son of Sarah (née Strauss), who came from Austria, and Harold "Harry" Arshawsky, a dressmaker and photographer from Russia. The family was Jewish and settled in New Haven, Connecticut, where Shaw grew up. He bought a saxophone with money earned in a grocery store and began to learn it at 13, switched to clarinet at 16, and left home to tour with a band. In 1925 he was with Johnny Cavallaro's dance band, and from the later 1920s he worked in Cleveland with Austin Wylie's orchestra, becoming its music director and arranger. In 1929 and 1930 he played with Irving Aaronson's Commanders, where he was exposed to symphonic music, then returned to New York, joined jam sessions with the stride pianist Willie "The Lion" Smith, and by 1931 was a busy studio musician. He joined Roger Wolfe Kahn's orchestra in 1932 and stepped away from music in 1934 to write a book before money problems brought him back.

In May 1936 Shaw played at an all-star swing concert at New York's Imperial Theatre and surprised the audience by performing his own "Interlude in B-flat" with a string quartet and a rhythm section, an early example of what was later called Third Stream. He built his first orchestra on that idea, adding strings to a Dixieland-style front line, but it broke up in early 1937. A conventional big band followed, with Georgie Auld and Tony Pastor on tenor saxophone, and after his Brunswick contract lapsed at the end of 1937 he signed with RCA Victor's Bluebird label. In March 1938 he hired Billie Holiday, who had left the Count Basie Orchestra a month earlier, making her one of the first Black women to sing full time with a white orchestra and the first to tour the segregated South in that role. Shaw had already played clarinet on four of her Vocalion sides in July 1936. She recorded one side with his band, "Any Old Time," and left in November 1938 after being told to use the service elevator at New York's Lincoln Hotel. Helen Forrest joined the band the same year, and the drummer Buddy Rich arrived in 1939.

On July 24, 1938, at RCA Victor's Studio 2 in New York, the band recorded Cole Porter's "Begin the Beguine" in an extended arrangement by Jerry Gray. The company was doubtful about so long a record and issued it as the flip side of "Indian Love Call," but it became a best seller and made Shaw a national star. DownBeat readers voted his band the best swing band of 1938, and he headlined a CBS radio series, with Robert Benchley as host, from November 1938 to November 1939. Shaw resented having to play the same hits night after night. In November 1939 he walked off the bandstand of the Cafe Rouge at New York's Hotel Pennsylvania in the middle of a broadcast, quit the band two days later, and went to Mexico; Pastor was soon coaxed into leading a band of his own. Rich had already moved on to Tommy Dorsey's orchestra in 1939.

Back in Hollywood in 1940, Shaw recorded "Frenesi" with strings and woodwinds on March 3 and led the band on the Burns and Allen radio show. He formed a small group from within the band, named the Gramercy Five after his telephone exchange, with Johnny Guarnieri on harpsichord, Billy Butterfield on trumpet and Al Hendrickson on guitar; their session of September 3, 1940 produced "Summit Ridge Drive," one of his million-selling records. He played himself in the Fred Astaire film Second Chorus (1940), for which he recorded "Concerto for Clarinet" on December 17, and his string-orchestra "Star Dust," with a trumpet solo by Butterfield, became one of his best-known records. In June 1941 his orchestra accompanied Lena Horne on two Victor sides. That September he formed a 31-piece orchestra with strings whose members included Hot Lips Page, Max Kaminsky, Georgie Auld, Dave Tough, Jack Jenney, Ray Conniff and Guarnieri. When news of Pearl Harbor reached him during a matinee in Providence, Rhode Island, on December 7, 1941, he gave the band two weeks' notice and joined the Navy.

From 1942 to 1944 Shaw led a Navy band in the Pacific, playing for service personnel, at times four concerts a day in battle zones including Guadalcanal, until a medical discharge in early 1944. The new Hollywood band he formed that year was a modern big band without strings, and its soloists included Roy Eldridge, Dodo Marmarosa and Barney Kessel; the revived Gramercy Five recorded again in January 1945. After his RCA contract ended in August 1945 he moved to Musicraft, and his 1946 sessions there featured the singer Mel Tormé and his Mel-Tones, including "I Got the Sun in the Morning," before the band broke up. He premiered Norman Dello Joio's Concertante for Clarinet and Orchestra, which he had commissioned, with the Chautauqua Symphony on July 23, 1949, and later that year led a short-lived modern band that included Zoot Sims, Al Cohn, Don Fagerquist and Marmarosa. His last recordings as a player came in 1953 and 1954 with a new Gramercy Five that featured Tal Farlow or Joe Puma on guitar, Joe Roland on vibraphone and Hank Jones on piano. In July 1954 he toured Australia on a bill with Buddy Rich and Ella Fitzgerald, then stopped playing the clarinet and spent much of the rest of the 1950s in Europe.

Away from the bandstand, Shaw wrote. His autobiography, The Trouble with Cinderella, appeared in 1952, followed by the three short novels of I Love You, I Hate You, Drop Dead! (1965) and the story collection The Best of Intentions and Other Stories (1989). He was married eight times, among others to the actresses Lana Turner and Ava Gardner, to Betty Kern, daughter of the songwriter Jerome Kern, and to the novelist Kathleen Winsor; his last wife was the actress Evelyn Keyes. In 1953 he was called before the House Un-American Activities Committee, which was investigating the World Peace Council. In 1968 he returned to a studio to conduct, without playing, a Capitol album of his late-1930s hits with veteran swing-era musicians. In 1983 he assembled a new orchestra with the clarinetist Dick Johnson as soloist and leader, which made its debut on New Year's Eve 1984 at the Glen Island Casino in New Rochelle, New York, and he fronted it for a few years. Brigitte Berman's documentary Artie Shaw: Time Is All You've Got (1985) won an Academy Award. He received a Grammy Lifetime Achievement Award in 2004 and passed away in Thousand Oaks, California, on December 30, 2004, at age 94; he had lived in its Newbury Park section. The University of Arizona holds his music library of more than 700 scores and parts.

Shaw treated the big band as a place to experiment as well as to dance. He wrote for strings and woodwinds, used a string quartet and rhythm section on "Interlude in B-flat," a use of strings that has been attributed to the influence of Igor Stravinsky; "Concerto for Clarinet" closes on a celebrated altissimo C. His theme, the minor-key "Nightmare," was an unusual choice for a hit-making leader and may have influenced a vamp in Monty Norman's "James Bond Theme." The Gramercy Five, with harpsichord and trumpet in front, made a lightly swinging small group out of the band. Shaw complained in print that he liked the music but not the business of music, which helps explain why each of his bands was short-lived. AllMusic calls him one of jazz's finest clarinetists, and Duke Ellington's longtime clarinetist Barney Bigard named him his favorite clarinet player.

Shaw is routinely paired with Benny Goodman, and both Wikipedia and Britannica describe his popularity as rivaling Goodman's. Fans answered Goodman's nickname "King of Swing" by calling Shaw the "King of the Clarinet," and Shaw said the two titles ought to be reversed, arguing that Goodman played clarinet while he played music. That is a rivalry for audiences and in musical ambition, and the sources do not describe a personal feud. The two men's circles overlapped: Helen Forrest sang with Shaw in 1938 and 1939 and then with Goodman, and the vibraphonist Teddy Charles, the pianist Hank Jones and the saxophonist Zoot Sims worked in both bands at different times.