In 1832, the initial non-denominational all-male institution began its first classes near City Hall based on a curriculum focused on a secular education. The university later moved and has maintained its main campus in Greenwich Village surrounding Washington Square Park, but was forced to sell its University Heights campus in the Bronx in 1973. Since then, the university has added a division in Brooklyn's MetroTech Center and graduate schools throughout Manhattan. NYU has become the largest private university in the United States by enrollment, with a total of 51,848 enrolled students, including 26,733 undergraduate students and 25,115 graduate students, in 2019. NYU also receives the most applications of any private institution in the United States and admissions is considered highly selective.

NYU is organized into 10 undergraduate schools, including the College of Arts & Science, Gallatin School, Steinhart School, Stern School of Business, Tandon School of Engineering, and the Tisch School of Arts. NYU's 15 graduate schools includes the Grossman School of Medicine, School of Law, Wagner Graduate School of Public Service, School of Professional Studies, School of Social Work, Rory Meyers School of Nursing, and Silver School of Social Work. The university's internal academic centers include the Courant Institute of Mathematical Sciences, Center for Data Science, Center for Neural Science, Clive Davis Institute, Institute for the Study of the Ancient World, Institute of Fine Arts, and the NYU Langone Health System. NYU is a global university with degree-granting campuses in NYU Abu Dhabi and NYU Shanghai, and academic centers in Accra, Berlin, Buenos Aires, Florence, London, Los Angeles, Madrid, Paris, Prague, Sydney, Tel Aviv, and Washington, D.C.

Past and present faculty and alumni include 38 Nobel Laureates, 8 Turing Award winners, 5 Fields Medalists, 31 MacArthur Fellows, 26 Pulitzer Prize winners, 3 heads of state, a U.S. Supreme Court justice, 5 U.S. governors, 4 mayors of New York City, 12 U.S. Senators, 58 members of the U.S. House of Representatives, two Federal Reserve Chairmen, 38 Academy Award winners, 30 Emmy Award winners, 25 Tony Award winners, 12 Grammy Award winners, 17 billionaires, and seven Olympic medalists The university has also produced six Rhodes Scholars, three Marshall Scholars, 29 Schwarzman Scholars, and one Mitchell Scholar.