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The analysis of dynamic games hinges on assumptions about players’ actions and beliefs at information sets that are not expected to be reached during game play. However, under the standard assumption that players are sequentially rational, these assumptions cannot be tested on the basis of observed, on-path behavior. This paper introduces a novel optimality criterion, structural rationality, which addresses this concern. In any dynamic game, structural rationality implies sequential rationality. If players are structurally rational, assumptions about on-path beliefs concerning off-path actions, as well as off-path beliefs, can be tested via suitable “side bets.” Structural rationality can also be characterized via trembles, or belief perturbations. Finally, structural rationality is consistent with experimental evidence about play in the extensive and strategic form, and justifies the use of the strategy method (Selten, 1967) in experiments.