n this talk we investigate the use of Trefftz methods for the numerical discretization of wave propagation problems in the time-domain. Trefftz methods instead of usual local polynomial approximation spaces, make use of approximation spaces containing locally exact solutions to the differential equation. Recently a number of space-time Discontinuous Galerkin (DG) methods have been developed for acoustic and electromagnetic waves. We present a Trefftz interior penalty dG method for the acoustic wave equation in the second order form. Full stability and convergence analysis for this formulation is available which we brifely present here. We further discuss in this talk the possibility of extending Trefftz methods to more general wave equations. The talk concludes with a set of numerical experiments in one- and two-spatial dimensions. This is joint work with E.H. Georgoulis (Leicester and Athens) and O. Lijoka (Edinburgh).