Columbia was established as King's College by a royal charter from King George II of Great Britain in reaction to the founding of Princeton College. It was renamed Columbia College in 1784 following the American Revolution, and in 1787 was placed under a private board of trustees headed by former students Alexander Hamilton and John Jay. In 1896, the campus was moved to its current location in Morningside Heights and renamed Columbia University.
Columbia scientists and scholars have played an important role in scientific breakthroughs including the brain-computer interface; the laser and maser nuclear magnetic resonance; the first nuclear pile; the first nuclear fission reaction in the Americas; the first evidence for plate tectonics and continental drift; and much of the initial research and planning for the Manhattan Project during World War II. Columbia is organized into twenty schools, including four undergraduate schools and 16 graduate schools. The university's research efforts include the Lamont–Doherty Earth Observatory, the Goddard Institute for Space Studies, and accelerator laboratories with major technology firms such as IBM. Columbia is a founding member of the Association of American Universities and was the first school in the United States to grant the M.D. degree. With over 14 million volumes, Columbia University Library is the third-largest private research library in the United States.

The university's endowment stands at $11.26 billion in 2020, among the largest of any academic institution. As of October 2020, Columbia's alumni, faculty, and staff have included: five Founding Fathers of the United States—among them a co-author of the United States Constitution and a co-author of the Declaration of Independence; three U.S. presidents; 29 foreign heads of state; ten justices of the United States Supreme Court, one of whom currently serves; 96 Nobel laureates; five Fields Medalists; 122 National Academy of Sciences members; 53 living billionaires; eleven Olympic medalists; 33 Academy Award winners; and 125 Pulitzer Prize recipients.