This paper derives from our joint interest in understanding how scientific mobility affects developing countries. Many authors have addressed the topic previously, both from an economic and from a sociological perspective. However, recent literature evinces dissatisfaction with both analytical frameworks and the framing of public policies addressing the brain drain problematic. This paper is a contribution to understanding the historical and theoretical foundations of the “brain drain” debate. We aim to improve conceptual clarity regarding the itinerancy of human beings and the mobilization of human capital. We develop a critical review of the economics of the brain drain, highlighting the work of some key early thinkers and pointing out the way in which subsequent work has taken up selected aspects of their approaches leaving other challenges aside. We then consider the diaspora networks literature, which is characterized as taking a “connectionist” approach to the brain drain. We identify two fundamental problems: the sidelining of complementarity and context dependency as basic properties of human capital; and a failure to adequately disentangle the concepts of human resources for science and technology (HRST) and human capital in academic and policy discourse about the brain drain.