Following the insights of Faure–Sjoestrand and Tsujii,microlocal/semiclassical methods have proved themselves very useful inthe study of closed and open smooth hyperbolic systems. We willexplain how they give a simple proof of the meromorphy of Ruelle zetafunction for Anosov flow (and indicate the ideas behind the Axiom Acase), show stochastic stability of Ruelle resonances, and explain theorder of vanishing of the zeta function at zero in the case ofnegatively curved surfaces (showing in particular that the lengthspectrum determines the genus).