Observed international investment positions and cross-country heterogeneity in rates of return to capital are hard to reconcile with frictionless capital markets. In this paper, we develop a theory of international capital allocation: a multi-country dynamic spatial general equilibrium model in which the entire network of cross-border investment is endogenously determined. Our model features cross-country heterogeneity in fundamental risk, a demand system for international assets, and frictions that cause segmentation in international capital markets. We measure frictions affecting international investment and apply our model to data from nearly 100 countries, using a new dataset of international capital taxes and cultural, linguistic, and geographic distances between countries (geopoliticaldistance.org). Our model performs well in reproducing the composition of international portfolios, the cross-section of home bias and rates of return to capital, and other key features of international capital markets. Finally, we carry out counterfactual exercises: we show that barriers to international investment reduce world output by 7% and raise the cross-country dispersion of capital per employee, contributing in a meaningful way to global inequality.