In this paper we analyse the trends in Foreign Direct Investment (FDI) flows worldwide across sectors and across value-chain activities, with a particular focus on low- and middle-income countries in comparison with advanced countries. We begin by discussing the growing fragmentation of global production and the opportunities this presents to today's developing countries for benefiting from FDI. Our review of the literature on knowledge spillovers via FDI indicates that spillovers typically occur along the value chain, from foreign firms to their local suppliers or clients but not to their competitors, and that tapping into the technological resources of foreign firms is not an automatic process but hinges on a few host-economy characterist...