The concept of power is central to international relations. Yet disciplinary discussions tend to privilege only one, albeit important, form: an actor controlling another to do what that other would not otherwise do. By showing conceptual favoritism, the discipline not only overlooks the different forms of power in international politics, but also fails to develop sophisticated understandings of how global outcomes are produced and how actors are differentially enabled and constrained to determine their fates. We argue that scholars of international relations should employ multiple conceptions of power and develop a conceptual framework that encourages rigorous attention to power in its different forms. We first begin by producing a taxonomy of power. Power is the production, in and through social relations, of effects that shape the capacities of actors to determine their circumstances and fate. This general concept entails two crucial, analytical dimensions: the kinds of social relations through which power works (in relations of interaction or in social relations of constitution); and the specificity of social relations through which effects are produced (specific/direct or diffuse/indirect). These distinctions generate our taxonomy and four concepts of power: compulsory, institutional, structural, and productive. We then illustrate how attention to the multiple forms of power matters for the analysis of global governance and American empire. We conclude by urging scholars to beware of the idea that the multiple concepts are competing, and instead to see connections between them in order to generate more robust understandings of how power works in international politics.