Benjamin Landon - Harvard University Dyson Brownian motion is a stochastic eigenvalue dynamics and the basis of the dynamical approach to random matrix theory. We review recent results on the local statistics of Dyson Brownian motion, as well as how these results are applied to prove the universality of general random matrix ensembles. Based on joint work with Z. Che, J. Huang, P. Sosoe and H.-T. Yau.