Craven graduated from Simpson College in 1908. He earned an M.A. from Harvard in 1914 and a Ph.D. from the University of Chicago in 1923. He taught at Michigan State University and the University of Illinois; in 1927, he joined the faculty of the University of Chicago, where he spent the rest of his career. His works included The Coming of the Civil War (University of Chicago Press, 1942) and The Growth of Southern Nationalism, 1848-1861 (LSU Press 1953).
The Organization of American Historians gives an annual award named after Professor Craven, "for the most original book on the coming of the Civil War, the Civil War years, or the Era of Reconstruction, with the exception of works of purely military history. The exception recognizes and reflects the Quaker convictions of Craven, President of the Organization of American Historians 1963-1964."
Craven's personal archives are part of the library collection at Simpson College.