Humanity faces a complex and dangerous global risk landscape, and many different terms and concepts have been used to make sense of it. One broad strand of research characterises how risk emerges from the complex global system, using concepts like systemic risk, Anthropocene risk, synchronous failure, negative social tipping points, and polycrisis. Another strand focuses on possible worst-case outcomes, using concepts like global catastrophic risk (GCR), existential risk, and extinction risk. Despite their clear relevance to each other, only limited connections have been made between these two strands. Here we provide a framework which synthesises the two and shows how emergent properties of the global system contribute to the risk of global catastrophic outcomes. Specifically, the global system generates hazards, amplification, vulnerability, and latent risk, as well as challenges for GCR assessment and mitigation. This systemic lens helps us understand the origins of GCR, provides a useful interface between two deeply related but infrequently connected bodies of work, and provides important insights for risk reduction.