In recent decades, advances in information and communication technology and falling trade barriers have led firms to retain within their boundaries and in their domestic economies only a subset of their production stages. A key decision facing firms worldwide is the extent of control to exert over the different segments of their production processes. We describe a property-rights model of firm boundary choices along the value chain that generalizes Antràs and Chor (2013). To assess the evidence, we construct firm-level measures of the upstreamness of integrated and non-integrated inputs by combining information on the production activities of firms operating in more than 100 countries with Input-Output tables. In line with the model's predictions, we find that whether a firm integrates upstream or downstream suppliers depends crucially on the elasticity of demand for its final product. Moreover, a firm's propensity to integrate a given stage of the value chain is shaped by the relative contractibility of the stages located upstream versus downstream from that stage, as well as by the firm's productivity. Our results suggest that contractual frictions play an important role in shaping the integration choices of firms around the world.