Evolution Strategies (ESs) have recently become popular for training deep neural networks, in particular on reinforcement learning tasks, a special form of controller design. Compared to classic problems in continuous direct search, deep networks pose extremely high-dimensional optimization problems, with many thousands or even millions of variables. In addition, many control problems give rise to a stochastic fitness function. Considering the relevance of the application, we study the suitability of evolution strategies for high-dimensional, stochastic problems. Our results give insights into which algorithmic mechanisms of modern ES are of value for the class of problems at hand, and they reveal principled limitations of the approach. They are in line with our theoretical understanding of ESs. We show that combining ESs that offer reduced internal algorithm cost with uncertainty handling techniques yields promising methods for this class of problems.