The essential function of money is its role as a medium of exchange. We formalize this idea using a search-theoretic equilibrium model of the exchange process that captures the "double coincidence of wants problem" with pure barter. One advantage of the framework described here is that it is very tractable. We also show that the model can be used to address some substantive issues in monetary economics, including the potential welfare-enhancing role of money, the interaction between specialization and monetary exchange, and the possibility of equilibria with multiple fiat currencies.