Many practical optimization problems involve decision-making under uncertainty and risk. We present two classes of such stochastic optimization problems, namely two-stage stochastic integer programming and chance-constrained programming. These problems result in large-scale mixed-integer programming formulations with certain structures. For each class of problems, we review mixed-integer programming techniques that enable effective solution approaches that exploit the underlying structures. These techniques span disjunctive programming, Gomory cuts, submodularity, mixing sets, mixed-integer conic programming, and Benders decomposition.