Graves trained to be an architect at the University of Cincinnati (Ohio) and at Harvard University (Cambridge, Mass.), earning a master's degree at Harvard in 1959. He then studied in Rome from 1960 to 1962 and upon his return to the United States took a teaching position at Princeton University (N.J.), becoming a full professor there in 1972.

Graves began his career in the 1960s as a creator of private houses in the abstract and austere style of orthodox Modernism, his compositions influenced by the work of Le Corbusier (Corbusier, Le). In the late 1970s, however, Graves began to reject the bare and unadorned Modernist idiom as too cool and abstract, and he began seeking a richer architectural vocabulary that would be more accessible to the public. He soon drew remarkable attention with his designs for several large public buildings in the early 1980s. The Portland Public Service Building (usually called the Portland Building) in Portland, Ore. (1980), and the Humana Building in Louisville, Ky. (1982), were notable for their hulking masses and for Graves's highly personal, Cubist interpretations of such classical elements as colonnades and loggias. Though somewhat awkward, these and other of Graves's later buildings were acclaimed for their powerful and energetic presence.

By the mid-1980s Graves had emerged as arguably the most original and popular figure working in the postmodernist idiom. He executed architectural and design commissions for clients around the world. In the early 1980s he created a playful and iconic teakettle (as well as a number of additional products) for the Alessi design firm, and he later created a line of household items, including kitchenware and furniture, for the discount retailer Target.

Among his later large-scale projects were the restoration of the Washington Monument (2000) and the expansion of the Detroit Institute of Arts (completed 2007). In 2001 Graves was awarded the American Institute of Architects Gold Medal (AIA) for lifetime achievement.