A fundamental difficulty in stochastic optimization is the fact that decisions may not be able pin down the values of future "costs," but rather can only, within limits, shape their distributions as random variables. An upper bound on a ramdom "cost" is often impossible, or too expensive, to enforce with certainty, and so some compromise attitude must be taken to the violations that might occur. Similarly, there is no instant interpretation of what it might mean to minimize a random "cost", apart from trying to determine a lowest threshold which would be exceeded only to an acceptable degree. Clearly, it is essential in this picture to have a theoretical framework which provides guidelines about preferences and elucidates their mathematical pros and cons. Measures of risk, coming from financial mathematics but finding uses also in engineering, are the key. Interestingly, they relate also to concepts in statistics and estimation. For example, standard deviation can be replaced by a generalized measure of deviation which is not symmetric between ups and downs, as makes sense in applications in which overestimation may be riskier than underestimation.