This paper develops a general equilibrium model of international trade that features selection across firms, products and countries. Firms’ export decisions depend on a combination of firm “productivity” and firm-product-country “consumer tastes”, both of which are stochastic and unknown prior to the payment of a sunk cost of entry. Higher-productivity firms export a wider range of products to a larger set of countries than lower-productivity firms. Trade liberalization induces endogenous reallocations of resources that foster productivity growth both within and across firms. Empirically, we find key implications of the model to be consistent with U.S. trade data.