A multi-scale asymptotic theory is derived for the evolution and interaction of surface gravity waves and currents in water of finite depth, under conditions typical of coastal shelf waters. The practical utility of the theory is that it provides a model with which shelf dynamics may be explored without the necessity of resolving features of the flow on space and time scales of the primary gravity-wave oscillations. The essential nature of the dynamical interaction is currents modulating the slowly evolving phase of the wave field and waves providing both phase-averaged forcing of long surface waves and vortex forces for the current evolution equations. Analogous relations are derived for material tracers and density stratification which include phase-averaged Stokes-drift advection. Illustrative solutions are analyzed for the special case of depth-independent currents.