Quantum ergodicity refers to results about delocalization of eigenfunctions of the Laplacian on compact manifolds of negative curvature. Work of Anantharaman and her collaborators in the last few years yields similar results about delocalization of eigenfunctions of the adjacency operator on finite graphs of degree at least 3. Such graphs may be viewed as discrete analogues of manifolds of negative curvature. In this talk we'll discuss some of the history of quantum ergodicity as well as the more recent results about graphs including some of the main ideas of the proof. Speaker(s): Carsten Peterson (University of Michigan)