Optimization and control problems often need to be formulated in a way that takes the uncertainty of the future into account in order to accurately reflect a "good" decision that can stand up to a variety of possible future outcomes. One way of including uncertainty in such problems treats the uncertain parameters as a random vector with an underlying probability distribution. Doing this creates a stochastic programming model which is
inherently infinite dimensional, or at best extremely large, in particular when many time
stages are present. In order to solve such problems, a good approximation framework is needed that encompasses various approaches such as sampling and analytical methods for various problem classes. Complementing this should be a development of solution procedures that exploit a problem's structure, for example taking advantage of convexity and decomposability wherever possible. This dissertation addresses these key issues in four parts.