Craig gained his first experience working in local theater before breaking into films as a junior draftsman on the uneven James Bond spoof "Casino Royale" (1967). He graduated to assistant art director and found his niche with the historical drama "Mary, Queen of Scots" (1971). In 1977 he became a full-fledged art director with Richard Attenborough's "A Bridge Too Far", assisting in creating the look of war-torn Holland. The film marked the beginning of a fruitful collaboration with Craig serving as production designer on every subsequent Attenborough film with the exception of "A Chorus Line" (1985). He won his first Oscar recreating eight decades of colonial India in "Gandhi" (1982) and went on to create colonial South Africa in "Cry Freedom" (1987). For "Chaplin" (1992), Craig designed a scheme that gradually added color as the film moved from depicting the world of silent films to more contemporary times. "Shadowlands" (1993) recreated a fusty 50s-era world of academia while "In Love and War" (1996) was another war-time would-be epic, complete with battle sequences and a period hospital.

Craig has won acclaim for his work with other directors as well. An atypical design was the comic-book inspired "Superman" (1978) for which Craig not only created the home planet of Krypton, with its futuristic look, but also the Middle American town of Smallville and the bustling, New York-inspired Metropolis. His stark designs of Victorian England created the world inhabited by "The Elephant Man" (1980, directed by David Lynch). "The Mission" (1986) recreated an 18th Century Jesuit church amid the Brazilian jungle. Craig earned a second Oscar for his elegant French Provincial decor for Stephen Frears' "Dangerous Liaisons" (1988) and won critical kudos for the Edwardian mansion, with its Gothic airs, contrasted with the lush, richly varied hues of "The Secret Garden" (1993). For Anthony Minghella's "The English Patient" (1996), he had the daunting task of creating the various worlds inhabited by the main characters, including the desert with its natural beauty, a bombed out Italian monastery and pre-World War II North Africa. Craig's designs worked on several levels and aided in creating that film's gorgeous visuals and he received a third Oscar for Best Art Direction.