abstract: In this talk, we will present existence results for a class of hyperbolic obstacle-type problems by using a variational approach in the spirit of minimizing movements. We consider both linear and nonlinear cases, as well as non-local (fractional) operators. We discuss some applications to singular limits of nonlinear wave equations and to nonlinear waves in adhesive phenomena. Results based on joint works with M. Bonafini, and with M. Novaga, G. Orlandi.