The growing interconnections among societies have facilitated the emergence of systemic crises, i.e., shocks that rapidly spread around the world and cause major disruptions. Advances in the interdisciplinary field of complexity can help understand the mechanisms underpinning systemic crises. This article reviews the most important concepts and findings from the pertinent literature. It demonstrates that an understanding of the nature of disruptions of globally interconnected systems and their implications is critical to prevent, react to, and recover from systemic crises. The resulting analytical framework is applied to two prominent examples of global systemic crises: the 2008 global financial crisis and the COVID-19 pandemic. The article provides evidence that relying on reactive and recovery capacities to face systemic crises is not sustainable because of the extraordinary costs they impose on societies. Efforts are needed to develop a multipronged strategy to strengthen our capacities to face systemic crises and address fundamental mismatches between the nature of global challenges and the necessary collective action to address these challenges.