Once the preserve of research in development economics, the study of highly skilled migration has recently attracted the interest of innovation scholars. The production of targeted data on migrant scientists, doctoral students and inventors is an important complement to official statistics. Highly skilled migrants have been found to exert a positive effect on destination countries, as measured by productivity, patenting or scientific publications. As for the impact on source countries of this migration, the US-centrism of the literature has biased research towards its migration source countries, such as China, India and other East Asian countries, all of which are developing countries. We know much less about migration to the USA from other developed countries, such as the European ones. Overall, the empirical evidence on inventors indicates that a diaspora network effect exists within receiving countries: inventors with the same ethnicity have a high propensity to collaborate among each other. But evidence on positive spillovers for their origin countries (brain gain) is mixed. Finally, more attention needs to be paid to intra-company migration and the role of multinationals. Although the first purpose of such intra-company international mobility is to transfer skills/knowledge to the headquarters/subsidiaries, with some externalities to the host economies, this topic remains a grey area in the literature of migration and innovation.