Artificial intelligence (AI) represents a technological upheaval with the potential to change human society. Because of its transformative potential, AI is increasingly becoming subject to regulatory initiatives at the global level. Yet, so far, scholarship in political science and international relations has focused more on AI applications than on the emerging architecture of global AI regulation. The purpose of this article is to outline an agenda for research into the global governance of AI. The article distinguishes between two broad perspectives: an empirical approach, aimed at mapping and explaining global AI governance; and a normative approach, aimed at developing and applying standards for appropriate global AI governance. The two approaches offer questions, concepts, and theories that are helpful in gaining an understanding of the emerging global governance of AI. Conversely, exploring AI as a regulatory issue offers a critical opportunity to refine existing general approaches to the study of global governance.