Arithmetic quantum chaos concerns the limiting behavior of a sequence of automorphic forms with parameters tending off to infinity. It is now known in many cases that the mass distributions of such forms equidistribute. Unfortunately, the known rates of equidistribution are typically weak (ineffective or logarithmic). I will discuss the problem of obtaining strong rates (power savings) and the related subconvexity problem, emphasizing recent progress concerning the level aspect on hyperbolic surfaces.