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We investigate the importance of worldwide demographic evolutions in shaping capital flows across countries and over time. Our lifecycle model incorporates cross-country differences in fertility and longevity as well as differences in countries' ability to borrow inter-temporally and across generations through social security. In this environment, global aging triggers uphill capital flows from emerging to advanced economies, while country-specific demographic evolutions reallocate capital towards countries aging more slowly. Our quantitative multi-country overlapping generations model explains a large fraction of capital flows across advanced and emerging countries and a substantial portion of the prolonged decline in the world interest rate.