This paper analyzes the factors underlying the evolution of the worldwide distribution of skills and their implications for global inequality. We develop and parameterize a two-sector, two-class, world economy model that endogenizes education and mobility decisions, population growth, and income disparities across and within countries. First, our static experiments reveal that the geography of skills matters for global inequality. Low access to education and sectoral misallocation of skills substantially impact income in poor countries. Second, we produce unified projections of population and income for the 21st century. Assuming the continuation of recent education and migration policies, we predict stable disparities in the world distribution of skills, slow-growing urbanization in developing countries and a rebound in income inequality. These prospects are sensitive to future education costs and to internal mobility frictions, which suggests that policies targeting access to all levels of education and sustainable urban development are vital to reduce demographic pressures and global inequality in the long term.