We discuss the policy questions and debate surrounding the role of international (foreign-born) graduate students in the productivity of universities, particularly in the United States. Concerns about national security have induced U.S. immigration authorities to limit the number of foreign doctoral students in science and engineering (S&E) departments in American research universities. This policy has reduced such enrollments beyond the decline already in evidence. Many university officials and business leaders are concerned that this reduction in foreign S&E students will damage domestic research capabilities and broader economic innovation. We review two recent studies of how the presence of international graduate students contributes to scientific journal publications and patents awarded to universities. Both studies, one using macro time-series data and one using micro student-level panel data, find strongly positive impacts, suggesting that limited access to foreign students could diminish knowledge creation and innovation. We then relate these results to educational and innovation policy in key East Asian economies. These nations have an opportunity to increase their enrollments of S&E students, which should enhance their own innovation capacities. However, to achieve full growth benefits from such changes in visa policy, governments need to ensure their economies are conducive to robust and competitive innovation processes.