Abstract: Increasing returns are as fundamental a cause of international trade as comparative advantage, but their role has until recently been neglected because of the problem of modeling market structure. Recently, substantial theoretical progress has been made using three different approaches. These are the Marshallian approach, where economies are assumed external to firms; the Chamberlinian approach, where imperfect competition takes the relatively tractable form of monopolistic competition; and the Cournot approach of noncooperative quantity-setting firms. This chapter surveys the basic concepts and results of each approach. It shows that some basic insights are not too sensitive to the particular model of market structure. Although much remains to be done, we have made more progress toward a general analysis of increasing returns and trade than anyone would have thought possible even a few years ago.