The international linkages between banks play a crucial role in today’s global economy. Existing models explain these links on the basis of portfolio theory, in which banks diversify lending. These models have found only limited empirical support and do not speak to many relevant dimensions of the data. For example, they do not address heterogeneity in the degree to which banking sectors fund their foreign operations locally in foreign markets. This paper proposes an alternative theory to explain banking across borders that is based on elements of international trade theory. In the model, banking across borders arises because countries differ in their relative factor endowments and in the efficiency of their banking sectors. Based on these differences, the pattern of foreign bank asset and liability holdings emerges endogenously. This parsimonious model provides a rationale for different dimensions of heterogeneity in foreign bank activities and clarifies the interpretation of international banking data. Its predictions are consistent with observed patterns in the data.