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This dissertation studies the role of firm-to-firm relationships in international trade, with a focus on two margins: (1) the dynamics of arms-length buyer-seller relationships, and (2) technology transfers within multinational firms. Chapter 1 studies the quantitative implications of frictions in the creation and destruction of firm-to-firm trading relationships for aggregate patterns of trade. I develop a structural model of trade in which the network of firm-level input-output linkages is endogenously determined, and use data on relationships between US firms to estimate the model's parameters. Counterfactual simulations of the model show that the endogenous adjustment of relationships dynamically amplifies the effects of changes in trade costs on trade volumes and welfare by more than three times. Chapter 2 documents that the hazard rate of relationship termination between firms in the US decreases with the age of the relationship as well as with buyer and seller size. I develop a general equilibrium model of trade which replicates this finding through a simple mechanism: firms engaged in trade receive relationship-specific productivity shocks that are both persistent and age-dependent. Using numerical simulations of the model, I show that these two features of the productivity process matter for the gains from trade, with welfare responding more strongly to trade costs when productivity growth is slower and when productivity shocks are more persistent. Chapter 3 studies the interaction between intellectual property rights (IPR) protection by governments and technology transfer (TT) by multinational firms to their subsidiaries. I develop a two-country model of trade and foreign direct investment, and show analytically the existence of two kinds of inefficiencies: one arising from governments' choices of IPR policies, and another from multinational firms' choices of TT. I find that the IPR and TT inefficiencies are characterized by under-provision of IPR protection and TT respectively, and that they are comparable in magnitude, amounting to as much as 4% of the gains from openness to trade and FDI. Advisors/Committee Members: Redding, Stephen J (advisor).