We investigate quantum Brownian motion sustained transport in both, adiabatically rocked ratchet systems and quantum stochastic resonance (QSR). Above a characteristic crossover temperature T0 tunneling events are rare; yet they can considerably enhance the quantum-noise-driven particle current and the amplification of signal output in comparison to their classical counterparts. Below T0 tunneling prevails, thus yielding characteristic novel quantum transport phenomena. For example, upon approaching T=0 the quantum current in Brownian motors exhibits a tunneling-induced reversal, and tends to a finite limit, while the classical result approaches zero without such a change of sign. As a consequence, similar current inversions generated by quantum effects follow upon variation of the particle mass or of its friction coefficient. Likewise, in this latter regime of very low temperatures the tunneling dynamics becomes increasingly coherent, thus suppressing the semiclassically predicted QSR. Moreover, nonadiabatic driving may cause driving-induced coherences and quantized resonant transitions with no classical analog.