  The study of wave propagation outside bounded obstacles uncovers the
existence of resonances for the Laplace operator, which are complex-valued
generalized eigenvalues, relevant to estimate the long time asymptotics of the
wave. In order to understand distribution of these resonances at high
frequency, we employ semiclassical tools, which leads to considering the
classical scattering problem, and in particular the set of trapped
trajectories. We focus on "chaotic" situations, where this set is a hyperbolic
repeller, generally with a fractal geometry. In this context, we derive fractal
Weyl upper bounds for the resonance counting; we also obtain dynamical criteria
ensuring the presence of a resonance gap. We also address situations where the
trapped set is a normally hyperbolic submanifold, a case which can help
analyzing the long time properties of (classical) Anosov contact flows through
semiclassical methods.
