We examine the empirical content of matching models of the labor market in which firms and work- ers are ex ante heterogeneous in the presence of symmetric uncertainty and learning about worker ability and human capital acquisition by workers. We allow ability and acquired human capital to be general across firms to varying degrees. We establish conditions under which the primitives of these models are identified simply based on data on workers’ jobs and wages. Through the lens of the models we consider, we investigate the ability of existing empirical measures of assortativeness of matching to detect the actual degree of sorting. We propose a new measure of matching assortativeness that accounts for the evolving uncertainty about workers’ ability and workers’ accumulating human capital. (Joint with Aureo De Paula, Elena Pastorino, Sergio Salgado)