I present a matching model with heterogeneous workers, firms, and worker-fim matches. The model generalizes the seminal Jovanovic (1979) model to the case of heterogeneous agents. The equilibrium wage is linear in a person-specific component, a firm-specific component, and a match specific component that varies with tenure. Under certain conditions, the equilibrium wage takes a simpler structure where the match specific component does not vary with tenure. I discuss fixed- and mixedeffect methods for estimating wage models with this structure on longitudinal linked employer-employee data. The fixed effect specification relies on restrictive identification conditions, but is feasible for very large databases. The mixed model requires less restrictive identification conditions, but is feasible only on relatively small databases. Both the fixed and mixed models generate empirical person, firm, and match effects with characteristics that are consistent with predictions from the matching model; the mixed model moreso than the fixed model. Shortcomings of the fixed model appear to be artifacts of the identification conditions.