Wave streaming is a near-bottom mean current induced by the bottom drag on surface gravity waves. Wave variations include the variations in wave heights, periods, and directions. Here we use numerical simulations to study the effects of wave streaming and wave variations on the circulation that is driven by incident surface waves. Wave streaming induces an inner-shelf Lagrangian overturning circulation, which links the inner shelf with the surf zone. Wave variations cause alongshore-variable wave breaking that produces surf eddies; however, such eddies can be suppressed by wave streaming. Moreover, with passive tracers we show that wave streaming and wave variations together enhance the cross-shelf material transport.