Abstract This paper surveys work on reputations in repeated games of incomplete information. We first develop the adverse-selection approach to reputations in the context of a long-lived player, who may be a “normal” type or one of a number of “commitment” types, and who faces a succession of short-lived players. We use entropy-based arguments both to establish a lower bound on the equilibrium payoff of the long-lived player (demonstrating ex ante reputation effects) and to show that this lower bound is asymptotically irrelevant under imperfect monitoring (demonstrating the impermanence of reputation effects). The chapter continues by examining the (necessarily weaker) reputation results that can be established for the case of two long-lived players, and by examining variations in the model under which reputation effects can persist indefinitely. The chapter closes with brief remarks on alternative approaches.