I will introduce the problem of quantum chaos on manifolds, especially in the case of locally symmetric spaces, i.e. spaces of the form $\Gamma\G/K$ where $\Gamma$ is a lattice in the s.s. Lie group $G$. For certain ("congruence") lattices there exists a discrete structure on this space which parallels the differential one, leading to the natural special case of arithmetic quantum chaos. I will give some ideas of the current approach to proving equidistribution in this case, based on the work of Lindenstrauss and Bourgain.