We investigate a model of one-to-one matching with transferable utility when some of the characteristics of the agents are unobservable to the analyst. We allow for a wide class of distributions of unobserved heterogeneity, subject only to a separability assumption that generalizes Choo and Siow (2006). We first show that the stable matching maximizes a social gain function that trades off exploiting complementarities in observable characteristics and matching on unobserved characteristics. We use this result to derive simple closed-form formulæ that identify the joint surplus in every possible match and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. We formulate a parametric version of the model and show several estimation techniques. We discuss computational and inference issues and provide efficient algorithms. Finally, we revisit Choo and Siow’s empirical application to illustrate the potential of our more general approach.