Constable got his Bachelor of Arts at Harvard University in 1950 and his Doctor of Philosophy at the same University in 1957.
Giles taught at the University of Iowa from 1955 to 1958 and at Harvard University from 1958 to 1984. He was the Henry Charles Lea-Professor of Medieval History at Harvard University from 1966 to 1977. From 1977 to 1984 he was Director of the Dumbarton Oaks Research Library. He joined the faculty of the Institute for Advanced Studies as a Medieval History Professor in the School of Historical Studies in 1985.
In 1959 Giles married Esther Van Horne Young, with whom he has two children, Olivia Renie and John Van Horne.