In this talk I’ll first go over some problems and related results in quantum chaos. Then I’ll explain how one can combine Quantum Ergodicity and Bochner’s theorem to prove that the number of nodal domains of quantum ergodic sequence of even eigenfunctions tends to infinity as the eigenvalue λ → +∞. In particular, this implies that the number of nodal domains of Maass-Hecke eigenforms grows with the eigenparameter. This talk is based on the joint works with S. Zelditch and with S. Jang.