We investigate the importance of worldwide demographic evolutions in shaping capital flows across countries. Our lifecycle model incorporates crosscountry 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 long-term capital flows across advanced and emerging countries.