We develop a model of monetary exchange where, as in the random matching literature, agents trade bilaterally and not through centralized markets. Rather than assuming they match exogenously and at random, however, we determine who meets whom as part of the equilibrium. We show how to formalize this process of directed matching in dynamic models with double coincidence problems, and present several examples and applications that illustrate how the approach can be used in monetary theory. Some of our results are similar to those in the random matching literature; others differ significantly.