While working on the doctorate, Cuno worked as Assistant Curator of Prints at the Harvard Art Museums from 1980 to 1983. In that final year, he was hired as Assistant Professor of Art History at Vassar College, a position that he held until 1986.
Cuno quickly began an illustrious career in museum directorship, serving as the director of many notable institutions within the United States and abroad. He first served as director of the Grunwald Center for Graphic Arts at the Hammer Museum from 1986 to 1989, and the Hood Museum of Art until 1991. Cuno was then appointed Elizabeth and John Moors Cabot Director of the Harvard Art Museums from 1991 to 2002, replacing Edgar Peters Bowron, and then moved on to The Courtauld Institute of Art for a year from 2003 to 2004, succeeding Eric Fernie. While at Harvard, he was elected to the American Academy of Arts and Sciences in 2001. He left the Courtauld to head the Art Institute of Chicago as Eloise W. Martin Director until 2011, replacing James N. Wood. In that final year, Cuno became the President and Chief Executive Officer of the J. Paul Getty Trust, and retired as of July 31, 2022.[5]