Crow was born in Chicago in 1948, and moved to San Diego, California in 1961.

His work from this period includes his books Painters and Public Life in Eighteenth Century Paris (1985) and Emulation: Making Artists for Revolutionary France (1995).

More recently, his work has involved modern and contemporary American and British art.

In a return to his earlier field, he delivered the 2015 Andrew W. Mellon Lectures at the National Gallery, Washington, on the subject, "Restoration as Event and Idea: Art in Europe 1814-1820."

[3] He served as director of the Getty Research Institute from 2000 to 2007, and started a new position as the Rosalie Solow Professor of Modern Art at New York University's Institute of Fine Arts in September 2007.