Leopold Stokowski was 80 years old when in 1962 he founded the ASO with a mission of making orchestral music accessible and affordable for everyone. He served as music director together with assistant Amos Meller until May 1972 when he returned to England. Subsequent music directors were Kazuyoshi Akiyama until 1978, followed by Moshe Atzmon, Giuseppe Patanè, and John Mauceri. In 1991, Catherine Comet was succeeded by Bard College president Leon Botstein.

Under music director Leon Botstein, the ASO expanded its mission, presenting concerts designed around various themes drawn from the visual arts, literature, politics, and history and reviving rarely performed masterworks through its Vanguard Series at Carnegie Hall. By preserving and restoring these works, the ASO makes them available for performance by other orchestras.

In New York, the ASO performs primarily at Carnegie Hall. At Bard College, the orchestra is the resident orchestra of the Richard B. Fisher Center for the Performing Arts, appearing in an annual winter subscription series. The ASO also takes part in the Bard Music Festival and SummerScape. The orchestra also offers a variety of music education programs at high schools in Manhattan and New Jersey. Over 150 recordings from ASO’s archives of live performances are available for download online. Concert notes documenting the ASO's performances of rare repertoire are also online. The collection came to the Archives from Lynne Meloccaro (class of 1985, executive director of the ASO) through Leon Botstein.