Revenue management models traditionally assume that future demand is unknown, but can be represented by a stochastic process or a probability distribution. Demand is however often difficult to characterize, especially in new or nonstationary markets. In this paper, we develop robust formulations for the capacity allocation problem in revenue management, using the maximin and the minimax regret criteria, under general polyhedral uncertainty sets. Our approach encompasses the following open-loop controls: partitioned booking limits, nested fare classes by origin-destination pairs, Displacement-Adjusted Virtual Nesting, and fixed bid prices. We also characterize the optimal booking policy under interval uncertainty; while partitioned booking limits are optimal under the maximin criterion, some nesting is desirable under the minimax regret criterion. Our numerical analysis reveals that robust controls can outperform the classical heuristics for network revenue management, while achieving the best performance in the worst case. Our models are scalable to solve practical problems, because they combine efficient solution methods (small mixed-integer and linear optimization problems) with very modest data requirements.