Horng-Tzer Yau is one of the world’s leading probabilists and mathematical physicists. He has worked on quantum dynamics of many-body systems, statistical physics, hydrodynamical limits and random matrices. Yau approached the problems of the quantum dynamics of many-body systems with tools he developed for statistical physics and probability. More recently, he has been the main driving force behind some stunning progress on bulk universality for random matrices. With L. Erdős and others, Yau has proven the universality of the local spectral statistics of random matrices, a problem that was regarded as the main challenge of random matrix theory. This argument applies to all symmetry classes of random matrices. In the special Hermitian case, T. Tao and V. Vu proved bulk universality concurrently. Yau’s work has been extended in many directions, for instance, his recent results concerning eigenvector statistics with P. Bourgade and spectral statistics of random graphs with R. Baerschmidt, A. Knowles and J. Huang.