This chapter introduces the Asian scientist migration system, focusing on the first stage of this system: the initial migration of aspiring Asian scientists to the West for training. The chapter explains how a well-established training pathway from Asia to the West had emerged in the second half of the twentieth century. The factors behind this emergence included the structural inadequacies of the scientific training system within the Asian home country, government- and university-driven opportunity structures in the West and in Asia that encouraged westward student migrations, the cumulative network effects driven by earlier cohorts of Asian student migrants in the West, and the widely circulating images of specific Western countries as scientifically advanced and welcoming. But the chapter also higlights the rising standards in science training in various Asian countries. With the growing stature of national research universities in select Asian countries, growing numbers of aspiring Asian scientists may choose to complete their doctoral training in their home country and only move to the West for postdoctoral training. Other aspiring scientists may choose to move within Asia for graduate training.