Fefferman took his BS at the University of Maryland and his PhD at Princeton with E.M. Stein (1969). After four years at the University of Chicago, Fefferman returned to the Princeton math department, where he has been ever since. He has worked on classical Fourier analysis, partial differential equations, several complex variables, quantum mechanics, conformal geometry, fluid dynamics, and computational geometry.

He has served as an editor of the Annals of Math and the Proceedings of the National Academy of Sciences and also served as chairman of the Princeton math department and a member of the MSRI Scientific Advisory Board. He has served on the MSRI Board of Trustees since 2006 and he was Chair of the Board (2007–10). His honors include the Alan Waterman Award, the Fields Medal, and the 2017 Wolf Prize. He is a member of the National Academy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society.