Many papers have documented a wage premium in foreign-owned and large firms. However, there is very little formal theory in the literature and empirical analyses are typically not based on hypotheses which are rigorously derived from theory. This paper contributes to the theory-empirics gap by developing a model that allows for two "pure" explanations for the wage premium. The first is a heterogenous-worker explanation along the lines of Yeaple (2005), where firms that select more scaleintensive technologies select ex-ante more productive workers. In this case, the wage premium is a pure selection phenomenon. The second explanation builds on the heterogeneous-firm model of Melitz (2003) combined with on-the-job learning as in Markusen (2001). Productivity differences between firms are internalized by ex-ante homogeneous workers, so the wage premium is a pure learning phenomenon due to ex-post higher productivity in foreign firms. Our model yields a number of precise empirical hypotheses. When these predictions are tested on Danish matched employer-employee data, we find that both explanations play a role in explaining the observed wage premium. Specifically, the foreign- and large-firm premiums explained by selection are in the neighborhood of 30-65% of the total premium, with the remainder consistent with learning. There is also considerable support for a number of other predictions specific to the worker-learning explanation.