This paper reviews the current understanding of moist orographic convection and its regulation by surface-exchange processes. Such convection tends to develop when and where moist instability coincides with sufficient terrain-induced ascent to locally overcome convective inhibition. The terrain-induced ascent can be owing to mechanical (airflow over or around an obstacle) and/or thermal (differential heating over sloping terrain) forcing. For the former, the location of convective initiation depends on the dynamical flow regime. In "unblocked" flows that ascend the barrier, the convection tends to initiate over the windward slopes, while in "blocked" flows that detour around the barrier, the convection tends to initiate upstream and/or downstream of the high terrain where impinging flows split and rejoin, respectively. Processes that destabilize the upstream flow for mechanically forced moist convection include large-scale moistening and ascent, positive surface sensible and latent heat fluxes, and differential advection in baroclinic zones. For thermally forced flows, convective initiation is driven by thermally direct circulations with sharp updrafts over or downwind of the mountain crest (daytime) or foot (nighttime). Along with the larger-scale background flow, local evapotranspiration and transport of moisture, as well as thermodynamic heterogeneities over the complex terrain, regulate moist instability in such events. Longstanding limitations in the quantitative understanding of related processes, including both convective preconditioning and initiation, must be overcome to improve the prediction of this convection, and its collective effects, in weather and climate models.