This work is dedicated to the memory of Donato Trigiante who has been the first teacher of Numerical Analysis of the second author. The authors remember Donato as a generous teacher, always ready to discuss with his students, able to give them profound and interesting suggestions.Here, we present a survey of numerical methods for differential systems with discontinuous right hand side. In particular, we will review methods where the discontinuities are detected by using an event function (so-called event driven methods) and methods where the discontinuities are located by controlling the local errors (so-called time-stepping methods). Particular attention will be devoted to discontinuous systems of Filippov’s type where sliding behavior on the discontinuity surface is allowed.