This lecture introduces the concept of risk measures and their use in stochastic optimization models to enable decision makers to seek decisions that are less likely to yield a highly undesirable outcome. In particular, we focus on coherent and convex risk measures, and demonstrate the duality relationship between such risk measures and distributionally robust stochastic optimization models. The specific examples of average value-at-risk (also known as conditional value-at-risk) and mean semideviation risk measures will be presented. Computational approaches to solve stochastic optimization models optimizing a convex risk measure will be presented, with particular focus on the average value-at-risk model.