We investigate the quantum transmission through laterally driven single- and double-barrier systems in the nonlinear regime of strong driving. A broad parameter range is explored, distinguishing in particular between different frequency regimes. The applicability of an effective, time independent, potential description in the high-frequency regime is explored. Moreover, we analyze in detail the inelastic processes and their dependence on parameters, resonant tunneling, and photon assisted tunneling. For the single-barrier problem we address driving laws that differ from the purely sinusoidal one. In this context, we encounter reduced spatial and temporal symmetries and demonstrate the corresponding effects on quantum pumping. For the double barrier, the focus of our studies lies on the impact of the variation in the relative phase of the barriers on the transmission.