In theory, financial globalization should contribute to a better allocation of saving and investment at the global level, while also enhancing the diversification of risks for global investors. In practice however, net saving transfers across countries remain substantially more limited than what theory suggests (« Feldstein-Horioka puzzle »). This article illustrates the most noteworthy developments of global saving and investment, taking a long run perspective; it highlights in particular the higher correlation between saving and investment across countries since the 2008 Global Financial Crisis. The article then summarizes the expected benefits of financial globalization and reviews the factors that hinder net saving transfers across countries. Finally, it concludes by outlining a few potential avenues to enhance these transfers without compromising financial stability.