Abstract. Semiclassical methods describe the transition from quantum to classical mechanics, and can be used to deduce information about a quantum system from the corresponding classical system. Many interesting dynamical properties, like ergodicity and mixing, unfold for large times, and in order to study their impact on the quantum system one needs semiclassical approximations which are uniform in time. The development of these methods poses one of the major challenges in semiclassics, and we will review the current state of the art and describe some new ideas which have been recently implemented for the Schroedinger equation on a manifold of negative curvature.