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. His honors include the Alan Waterman Award and the Fields Medal. He is a member of the National Academy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society.