Arithmetic quantum chaos concerns the limiting behavior of a sequence of automorphic forms on spaces such as the modular surface. It is now known in many cases (by work of Lindenstrauss, Holowinsky, Soundararajan and others) that the mass distributions of such forms equidistribute as the parameters tend off to infinity. Unfortunately, the known rates of equidistribution are typically weak (ineffective or logarithmic in the parameters). I will discuss the problem of obtaining strong rates (power savings) and the related subconvexity problem, emphasizing recent progress on the level aspect.