In this work we present and discuss theoretical models of redox molecular junctions that account for recent observations of nonlinear charge transport phenomena, such as hysteresis and hysteretic negative differential resistance (NDR). A defining feature in such models is the involvement of at least two conduction channels—a slow channel that determines transitions between charge states of the bridge and a fast channel that dominates its conduction. Using Marcus’ theory of heterogeneous electron transfer (ET) at metal–molecule interfaces we identify and describe different regimes of nonlinear conduction through redox molecular bridges, where the transferring charge can be highly localized around the redox moiety. This localization and its stabilization by polarization of the surrounding medium and/or conformational changes can lead to decoupling of the current response dynamics from the time scale of the voltage sweep (that is, the current does not adiabatically follow the voltage), hence to the appearance of memory (thermodynamic irreversibility) in this response that is manifested by hysteresis in current–voltage cycles. In standard voltammetry such irreversibility leads to a relative shift of the current peaks along the forward and backward voltage sweeps. The common origin of these behaviors is pointed out, and expressions of the threshold voltage sweep rates are provided. In addition, the theory is extended (a) to analyze the different ways by which such phenomena are manifested in single sweep cycles and in ensemble averages of such cycles and (b) to examine quantum effects in the fast transport channel.