  This paper is a survey on some recent aspects and developments in stochastic
control. We discuss the two main historical approaches, Bellman's optimality
principle and Pontryagin's maximum principle, and their modern exposition with
viscosity solutions and backward stochastic differential equations. Some
original proofs are presented in a unifying context including degenerate
singular control problems. We emphasize key results on characterization of
optimal control for diffusion processes, with a view towards applications. Some
examples in finance are detailed with their explicit solutions. We also discuss
numerical issues and open questions.
