Glenn Miller and His Orchestra was an American swing dance band that was formed by Glenn Miller in 1938. Arranged around a clarinet and tenor saxophone playing melody, and three other saxophones playing harmony, the band became the most popular and commercially successful dance orchestra of the swing era and one of the greatest singles-charting acts of the 20th century. As of 2025, Ray Anthony is the last surviving member of the orchestra.

Miller began professionally recording in New York City as a sideman in the hot jazz era of the late 1920s. With the arrival of virtuoso trombonists Jack Teagarden and Tommy Dorsey, Miller focused more on developing his arrangement skills. Writing for contemporaries and future stars such as Artie Shaw, and Benny Goodman, Miller gained prowess as an arranger by working in a variety of settings. Later, Miller largely improved his arranging and writing skills by studying under music theorist Joseph Schillinger.

In February 1937, Miller started an orchestra that briefly made records for Decca. With this group, Miller used an arrangement he wrote for British bandleader Ray Noble's American band in an attempt to form a clarinet-reed sound. This style developed over time, and eventually became known as the Glenn Miller sound. Frustrated with his agency over playing inconsistent bookings and lacking broad radio exposure, Miller gave the band notice in December 1937. Less than three months later, he was looking for members and forming a new band.

Miller began a partnership with Eli Oberstein, which led directly to a contract with Victor subsidiary Bluebird Records. Gaining fame at such engagements as the Paradise Restaurant and Frank Dailey–owned Meadowbrook and their corresponding nationwide broadcasts, Miller struck enormous popularity playing the Glen Island Casino in the summer of 1939. From late 1939 to mid-1942, Miller was the number-one band in the country, with few true rivals. Only Harry James' band began to equal Miller's in popularity as he wound down his career in the wake of the Second World War. The AFM strike prevented Miller from making any new recordings in the last two months of his band's existence, and they formally disbanded at the end of September 1942.

Miller's short-term chart successes have seldom been duplicated and his group's unprecedented dominance of early Your Hit Parade and Billboard singles charts resulted in 16 number-one singles and 69 Top Ten hits.