Most applications of game theory assume equilibrium, justified by presuming either that learning will have converged to one, or that equilibrium approximates people's strategic thinking even when a learning justification is implausible. Yet several recent experimental and empirical studies suggest that people's initial responses to games often deviate systematically from equilibrium, and that structural nonequilibrium “level-k” or “cognitive hierarchy” models often out-predict equilibrium. Even when learning is possible and converges to equilibrium, such models allow better predictions of history-dependent limiting outcomes. This paper surveys recent theory and evidence on strategic thinking and illustrates the applications of level-k models in economics. (JEL C70, D03, D82, D83)