He is best known for his work in theoretical condensed matter physics and statistical mechanics, and in particular for research on critical phenomena and conformal field theory. He was an undergraduate and postgraduate student at Downing College, University of Cambridge, before moving to the University of California, Santa Barbara, where he joined the faculty in 1977. In 1993, he moved to the University of Oxford, where until 2014 he was a Fellow of All Souls College (now Emeritus) and a Professor of Physics in the Rudolf Peierls Centre for Theoretical Physics.
He currently holds a Visiting Professorship at the University of California, Berkeley.
He is most known for his contributions to conformal field theory. The famous Cardy formula for black hole entropy, the Cardy formula in percolation theory, and the Cardy conditions in boundary conformal field theory are named after him.