One hallmark of chaos is sensitive dependence to initial conditions, the “butterfly effect.” We will discuss recent advances in our understanding of the quantum butterfly effect and its connection to the quantum physics of black holes. We will discuss a universal bound on the rate of development of quantum chaos motivated by these developments. Then we will briefly describe recent work on a connection between the late time behavior of black holes and the dynamics of random matrices. * Please note the new colloquium start time at 4 p.m.*