Introduction The notion of reputation found in common usage represents a concept that plays a central role in the analysis of games and markets with dynamic features. The purpose of this exposition is to describe how mathematical constructs roughly interpretable as reputations arise naturally as part of the specification of equilibria of sequential games and markets. In addition, several examples will be sketched, and a few of the economic applications surveyed. The main theme here is that reputations account for strong intertemporal linkages along a sequence of otherwise independent situations. Moreover, from examples one sees that these linkages can produce strategic and market behavior quite different from that predicted from analyses of the situations in isolation. The economic applications, for instance, indicate that a firm's reputation is an important asset that can be built, maintained, or “milked,” and that reputational considerations can be major determinants of the choices among alternative decisions. The key idea is that one's reputation is a state variable affecting future opportunities; moreover, the evolution of this state variable depends on the history of one's actions. Hence, current decisions must optimize the tradeoffs between short-term consequences and the longer-run effects on one's reputation. As the discussion proceeds, this general idea will be shown to have a concrete formulation derived from the analysis of sequential games. Semantics In common usage, reputation is a characteristic or attribute ascribed to one person (firm, industry, etc.) by another (e.g., “A has a reputation for courtesy”).