Philosophers are engaged in the project of interpreting physical theories. That is, they are concerned with the problem of how to go about associating physical content with the mathematical structures that are used to express physical theories. Interpreting quantum field theory has been thought to be especially problematic because the mathematical foundations of the theory are not yet well understood. Perturbative ultraviolet divergences, in particular, have been the source of much consternation. In this talk I will explain how resources from Epstein-Glaser renormalization can be used to show that these divergences are merely an artifact of the mishandling of the distributional character of field operators. This opens the path to interpreting quantum field theory, and more generally, to a better understanding of how physical content is associated with mathematical structure in physical theories.