Problems of finding optimal solutions under uncertainty described by random variables with a partial information on probability distributions are considered. The approach of distributionally robust optimization is described, which consists in constructing an ambiguity set from a priori information and using it in the worst-case constructions of risk measures for finding robust solutions. The reduction of initial problems with uncertainty to the corresponding problems of deterministic optimization using risk measures is considered. Problems of optimization by the reward-risk ratio and portfolio optimization are described. Contains some results of the use of polyhedral coherent risk measures in problems with uncertainty.