The park is named after the Damrosch family, a family of musicians. Performances take place at the Daniel and Florence Guggenheim bandshell, in the western end of the park above Amsterdam Avenue. The south side has street entrances, and the northeast corner of the park connects directly to the Center's central plaza.
The park is used for large events such as New York Fashion Week in August and February, the Lincoln Center Festival in July, Lincoln Center Out of Doors in August, and the Big Apple Circus October through January. Some local residents have argued that these events are inconsistent with the park's status as a park, and have sued to keep the park available to the public year round.