First, a model of horizontally and vertically integrated firms is developed. These firms are then embedded in a general equilibrium model of trading countries. It is shown how multinational corporations emerge as a result of differences across countries in factor compositions. Intersectoral, intraindustry, and intrafirm trade can coexist, and intrafirm trade takes place in invisibles (headquarter services) and intermediate inputs. It is shown how the various trade components depend on the structure of the world economy. The model predicts trade patterns which are close to observed trade patterns.