The study of international trade has made huge advances in recent decades by moving away from a perfectly competitive view of the world, and allowing for increasing returns and product diversity. However, in this effort it has borrowed very selectively from the theory of industrial organization. Both the “new trade theory revolution” of Krugman and others, and the more recent development of models with firm heterogeneity by Melitz and others, have entrenched the position of monopolistic competition as the dominant approach to modelling international trade. This ignores the insights of oligopoly theory, since it assumes that all firms are infinitesimal in scale, are equally likely to exit in a given period, and do not interact strategically. It also sits uneasily with a growing body of empirical work which shows that much of international trade is accounted for by very large firms.My project aims to bridge this gap by extending the theory of oligopoly and trade. Drawing on my past work, I propose to develop a new theoretical framework which recognizes the central role played by “superstar firms” while also allowing for entry of new firms and for interactions between sectors in general equilibrium. This involves three distinct strands. First is the development of models with a small number of large firms, interacting strategically with each other, while simultaneously competing against a “monopolistically competitive fringe” of small firms. Second is the application of these models to allow for a broader range of behaviour by large firms, including strategic investment in research and development, and a proliferation of products produced and markets served. And third is to use the techniques of monotone comparative statics to explore the properties of superstar-firm models, and to derive testable predictions from them.