Few-layer black phosphorus (BP) is a new two-dimensional material which is of great interest for applications, mainly in electronics. However, its lack of environmental stability severely limits its synthesis and processing. Here we demonstrate that high-quality, few-layer BP nanosheets, with controllable size and observable photoluminescence, can be produced in large quantities by liquid phase exfoliation under ambient conditions in solvents such as N-cyclohexyl-2-pyrrolidone (CHP). Nanosheets are surprisingly stable in CHP, probably due to the solvation shell protecting the nanosheets from reacting with water or oxygen. Experiments, supported by simulations, show reactions to occur only at the nanosheet edge, with the rate and extent of the reaction dependent on the water/oxygen content. We demonstrate that liquid-exfoliated BP nanosheets are potentially useful in a range of applications from ultrafast saturable absorbers to gas sensors to fillers for composite reinforcement.