GEOMETRY/DYNAMICAL SYSTEMSPeriodic bounce orbits are generalizations of billiard trajectories in the presence of a potential. Using an approximation technique by Benci-Giannoni we prove existence of periodic bounce orbits of prescribed energy. At the end of the talk I will sketch very recent work in which we allow much more general Lagrangian systems including magnetic and Finsler billiards. This is joint work with Marco Mazzucchelli.