We examine the implications of worker heterogeneity on the equilibrium matching process, using a directed search model. Worker abilities are selected from a general distribution, subject to some weak regularity requirements, and the firms direct their job offers to workers. We identify conditions under which some fraction of the workforce will be "unemployable": no firm will approach them even though they offer positive surplus. For large markets we derive a simple closed form expression for the equilibrium matching function. This function has constant returns to scale and two new terms, which are functions of the underlying distribution of worker productivities: the percentage of unemployable workers, and a measure of heterogeneity ().The equilibrium unemployment rate is increasing in and, under certain circumstances, is increasing in the productivity of highly skilled workers, despite endogenous entry. A key empirical prediction of the theory is that 1. We examine this prediction, using data from several countries.