A global extinction crisis may threaten the survival of most existing life forms. Influential discourses of ‘existential risk’ suggest that human extinction is a real possibility, while several decades of evidence from conservation biology suggests that the Earth may be entering a ‘sixth mass extinction event’. These conditions threaten the possibilities of survival and security that are central to most branches of International Relations. However, this discipline lacks a framework for addressing (mass) extinction. From notions of ‘nuclear winter’ and ‘omnicide’ to contemporary discourses on catastrophe, International Relations thinking has treated extinction as a superlative of death. This is a profound category mistake: extinction needs to be understood not in the ontic terms of life and death, but rather in the ontological context of be(com)ing and negation. Drawing on the work of theorists of the ‘inhuman’ such as Quentin Meillassoux, Claire Colebrook, Ray Brassier, Jean-Francois Lyotard and Nigel Clark, this article provides a pathway for thinking beyond existing horizons of survival and imagines a profound transformation of International Relations. Specifically, it outlines a mode of cosmopolitics that responds to the element of the inhuman and the forces of extinction. Rather than capitulating to narratives of tragedy, this cosmopolitics would make it possible to think beyond the restrictions of existing norms of ‘humanity’ to embrace an ethics of gratitude and to welcome the possibility of new worlds, even in the face of finitude.