It opened in 1978 as the Stony Brook University Fine Arts Center before being renamed in October 1988 after a $1.8 million donation from the Staller family.

The Staller Center contains three black-box theaters, a recital hall, the Paul W. Zuccaire Gallery and a professional 1,000-seat performance stage that features a 40-foot movie screen and is the site of the Stony Brook Film Festival.

The Staller Center has hosted several nationwide events such as the New York Science Fiction Forum in 1998 and more recently the Live Action Role Playing League's production of A Link to the Past.

[12] Joel also donated a $250,000 Bösendorfer Imperial grand piano to the Stony Brook University music department in 2013, and it currently rests in the Staller Center recital hall.

[19] In 2023, the Staller Center hosted tour dates from Corinne Bailey Rae, Pat Metheny, LeAnn Rimes and Celtic Woman's Tara McNeill.

Comedians Tom Segura and Kevin James and actors Leslie Odom Jr., Kristin Chenoweth and Evan Rachel Wood also performed.