As a youth in Chicago, Craig was an Eagle Scout, and also participated in both competitive swimming and judo. A more scholarly interest in Japan was piqued after the Second World War. While doing counterintelligence work for the United States Army in 1946 and 1947, he was stationed in Miyazaki and in Kyoto.While in Kyoto, he earned a third degree black belt in judo.
Craig earned an undergraduate degree in philosophy in 1949 at Northwestern University, where he was member of Phi Beta Kappa. While there, he set an NCAA freshman record in the 200 yard breaststroke. After college, the Fulbright Program made it possible for him to study economic history at the University of Strasbourg in Strasbourg, France. This was followed by two years (1951-53) as a graduate student at Kyoto University from 1951 through 1953.
Professor Craig became a member of Harvard's faculty in 1959 and then taught there for forty years, during which he was also a visiting professor at the University of Tokyo, the University of Kyoto, and Keio University.
He became the Harvard-Yenching Research Professor of Japanese History. In addition, he served as Director of the Reischauer Institute (1983-1985) and as Director of the Harvard-Yenching Institute (1976-1987).