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International order shapes our world, yet it is hard to know when and why it changes. I define international order as the governing arrangements among a group of states and non-state actors, including its fundamental rules, principles, and institutions. Nowhere is an order written down in a single document, or manifested in a single organization. It tends to exist in the same way that a digital picture consists of hundreds of pixels. As with pixels, parts of an international order can shift without necessarily changing the overall picture. This paper represents the first chapter of a book about how to identify and analyze changes in international order. It advances two big ideas. The first is conceptual: it develops a new theory for breaking down the complexity of world politics, called subsystems theory. International order exists within subsystems. The second is explanatory: I propose two variables to explain when and why international order changes: how much each of the actors benefits from participating in an order, and the punishments they can expect for noncompliance. I apply my theory to global oil politics, and to three other issue areas, to show both the depth and the breadth of the theory’s applications. I find that at the systemic level, international order exists only as a theme or themes across multiple subsystems.