Distributionally robust optimization is a framework that unifies robust optimization and stochastic programming. Compared to stochastic programming, the framework is based on stochastic modeling, but it only uses statistics from sampled data that are easier to obtain than a full stochastic model. The key assumption is that the underlying probability distribution belongs to a set of distributions (defined by the statistics), similar to conventional robust optimization. Naturally, distributionally robust optimization requires solving an infinite-dimentional optimization problem and is not amenable to numerical solutions. I have developed tractable numerical solutions for a very general class of distributionally robust optimization problems. The method has been applied to the problem of energy storage assignment in a power network in the presence of uncertain wind power generation.