This paper examines the evolving trends and policy dynamics of international student migration, focusing on their implications for STEM workforce development and innovation. While the United States has remained a leading destination for international students, recent years have seen a plateau or decline in incoming students, contrasted by growth in countries like Canada, Australia, and emerging hubs such as China and India. International students, particularly in STEM fields, play a critical role in shaping host countries' innovation ecosystems, often transitioning to permanent residents and STEM workers. We review immigration policies, including post-graduation work and residency pathways, highlighting their varying impacts on student inflows and innovation. Policies in Canada and Australia have until recently eased these transitions, while restrictive measures in the U.S. and U.K. have posed challenges. By documenting these trends and policy shifts, we identify gaps in the literature and outline directions for future research at the intersection of international education, immigration, and innovation.