We investigate a model of one-to-one matching with transferable utility and general unobserved heterogeneity. Under a separability assumption that generalizes Choo and Siow (2006), we first show that the equilibrium 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 formulae that identify the joint matching surplus and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. We provide efficient algorithms to compute the stable matching and to estimate parametric versions of the model. Finally, we revisit Choo and Siow’s empirical application to illustrate the potential of our more general approach.