The goal of this paper is twofold : rst a rapid introduction to the concept of hybrid system and second the presentation of a new direction in computer algebra that we have called hybrid computation. Hybrid computation can be seen as the application of the philosophy of hybrid systems to the eld of computation. We have focused our presentation on four directions that are actually developped in the MASH-project : Integration of ODE, Dynamic hybrid systems, Generalized splines and optimal control.