The school was founded by the Russo-Georgian-born choreographer George Balanchine, and philanthropists Lincoln Kirstein and Edward Warburg in 1934.

Children in the younger divisions are able to perform in various ballets with the company including George Balanchine's famous The Nutcracker, A Midsummer Night's Dream, Peter Martins's Swan Lake, and The Sleeping Beauty.

This started in 1965, when Alexandra Danilova sought and received approval from Balanchine to produce a spring workshop performance for the students.

][7][8] Some alumni include Mary Ellen Moylan, Maria Tallchief, Tanaquil LeClercq, Francisco Moncion, John Clifford,[9][10] Nicholas Magallanes,[11][12][13] Lois Bewley,[14] Jacques d'Amboise, Debra Austin, Margaret Severin-Hansen, SarahAnne Perel, Jillana, Allegra Kent, Arthur Mitchell, Wilhelmina Frankfurt, Patricia McBride, Alicia Holloway, Paul Frame, Peter Frame, Edward Villella, Suzanne Farrell, Kay Mazzo, Kathryn Morgan, Garielle Whittle, Helgi Tomasson, Fernando Bujones, Gelsey Kirkland, Heather Watts, Merrill Ashley, Lourdes Lopez, Jock Soto, Peter Boal, Olivia Boisson, Alexandra Waterbury, Victoria Rowell, Kyra Nichols, Darci Kistler, Patrick Bissell, Damian Woetzel, Ethan Stiefel, Wendy Whelan, Alan Bergman, Llanchie Stevenson, George Lee, Sarah Hay, Arlene Shuler, and Paloma Herrera as well as celebrities Sean Young, Ashlee Simpson, Macaulay Culkin, Lawrence Leritz, Vanessa Carlton, Yvonne Craig.

SAB students are chosen each year on the basis of their outstanding promise and a faculty member is honored for distinguished service.