The successful management of capital-intensive development and engineering projects requires a careful timing of the involved cash in- and outflows. To this end, the project management literature proposes to schedule the project activities so as to maximize their net present value (NPV), that is, the sum of all discounted cash flows. Traditionally, the literature on NPV maximization ignores the uncertainty inherent in the activity durations and cash flows. In this survey, we argue that this uncertainty should be accounted for explicitly, and we investigate the computational challenges involved in doing so. We then review the two major strands of literature on stochastic NPV maximization. The first set of papers provides optimal solutions under the assumption that the activity durations follow independent exponential distributions. The second strand of literature allows for generic distributions but focuses on suboptimal solutions. We conclude with a list of research questions that we believe deserve further attention