AbstractWhy are existing global governance structures “not fit for purpose” when it comes to addressing complex global catastrophic risks (CGCRs) such as climate breakdown, ecosystem collapse, or parasitic artificial general intelligence? This article argues that a deeper appreciation of these risks as complex—as opposed to complicated—is vital to an effective global governance response. It joins other IR scholarship seeking to invigorate a rigorous research agenda on complex system dynamics within world politics, highlighting the value of complexity theory, not simply as a contextual descriptor, but as a conceptual toolkit to inform CGCR governance research and action. Taking seriously the implications of “restricted complexity,” it interrogates why the legacy governing toolkit—the assumptions, heuristics, models, and practices conventionally employed to solve international collective action problems—are unlikely to suffice. It further draws laterally upon design science to offer a novel design model for governing complex systems, with broad application across global policy domains. A case study of the COVID-19 pandemic response illustrates the importance of supplementing inherited “complicated” governance system design and practices with design principles explicitly oriented to working with complexity, rather than against it. We contend that IR scholars and practitioners must update old ways of thinking in light of a complexification of the discipline. Such a shift involves both revisiting the design logics underlying how we build global governance structures, as well as pursuing a generative research agenda more capable of responding adequately to instability, surprise, and extraordinary change.