The dynamical evolution of short-period comets, and in particular of those belonging to the so-called Jupiter family, is reviewed. Encounters with Jupiter play a dominant role in determining the
dynamical fate of these objects, although, in some peculiar cases, also interactions with other planets may be important. Frequent although temporary librations around resonances with Jupiter are displayed by more than one third of short-period comets. Integrations of motion of observed comets, over a time span comparable with their lifetime as active objects, are compared with previous numerical investigations, to get insight into the non observed phases of the dynamical evolution of these objects.