Many practical optimization problems contain uncertain parameters. First, we give a short introduction into modelling issues in case that the uncertainty has a probabilistic background, i.e., that historical data or further probabilistic information is available (e.g., market prices or customer demands). Secondly, we introduce multistage stochastic programs as flexible models for many optimization problems under stochastic uncertainty, review some relevant theory and provide basic principles for their numerical solution. Finally, we discuss some recent challenges and results for such models, in particular, on the approximate representation of the stochastic input in form of scenario trees, on decomposition methods for large scale models, and on the incorporation of integer variables and of risk functions. Some numerical results for electricity portfolio optimization and airline revenue management are also discussed.