In this talk I will discuss some problems in Quantum Chaos and describe results in arithmetic settings where more can be proved. Given a compact, smooth Riemannian manifold (M,g) a central problem in Quantum Chaos is to understand the behavior of eigenfunctions of the Laplace-Beltrami operator in the limit as the eigenvalue tends to infinity. The Quantum Ergodicity Theorem of Shnirelman, Colin de Vediere, and Zelditch asserts that if the geodesic flow on M is ergodic then the mass of almost all of the eigenfunctions equidistributes. I will discuss problems which go beyond the Quantum Ergodicity Theorem such as quantum unique ergodicity and small scale quantum ergodicity in the setting of arithmetic surfaces such as the torus and modular curve.