In 1962 Milnor was awarded the Fields Medal for his work in the field of differential topology. He later went on to win the National Medal of Science (1967) and the Leroy P Steele Prize (1982).

He has been editor of the Annals of Mathematics since 1962 and has written books, on *Morse Theory*, *Characteristic Classes* (with Stasheff), *The h-cobordism theorem*, and *Dynamics in One Complex Variable*.