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This paper develops a multi-stage general-equilibrium model of global value chains (GVCs) and studies the specialization of countries within GVCs in a world with barriers to international trade. With costly trade, the optimal location of production of a given stage in a GVC is not only a function of the marginal cost at which that stage can be produced in a given country, but is also shaped by the proximity of that location to the precedent and the subsequent desired locations of production. We show that, other things equal, it is optimal to locate relatively downstream stages of production in relatively central locations. We also develop and estimate a tractable, quantifiable version of our model that illustrates how changes in trade costs affect the extent to which various countries participate in domestic, regional or global value chains, and traces the real income consequences of these changes.