We study the role of firm heterogeneity and imperfect competition for global production networks and the gains from trade. We develop a quantifiable trade model with two-sided firm heterogeneity, matching frictions, and oligopolistic competition upstream. More productive downstream buyers endogenously match with more upstream suppliers, thereby inducing tougher competition among them and enjoying superior sourcing outcomes. We then present consistent empirical evidence using highly disaggregated data on firms' production and trade transactions for France, Chile and China. Downstream French and Chilean buyers import higher values and quantities at lower prices as upstream Chinese markets become more competitive over time, with stronger responses by larger buyers. Chinese suppliers set lower prices and mark-ups to buyers that source from more suppliers. Counterfactual analyses indicate that lower barriers to entry upstream, lower matching costs, and lower trade costs amplify firm productivity and aggregate welfare downstream, with differential effects across firms. These effects operate through a combination of improved buyer-seller matches, gains from variety, and lower mark-ups. Global production networks thus generate greater impacts and cross-border spillovers from industrial policy and trade liberalization.