The crises that cities faceâ€”such as climate change, pandemics, economic downturn, and racismâ€”are tightly interlinked and cannot be addressed in isolation. This paper addresses compound urban crises as a unique type of problem, in which discrete solutions that tackle each crisis independently are insufficient. Few scholarly debates address compound urban crises and there is, to date, a lack of interdisciplinary insights to inform urban governance responses. Combining ideas from complex adaptive systems and critical urban studies, we develop a set of boundary concepts (unsettlement, unevenness, and unbounding) to understand the complexities of compound urban crises from an interdisciplinary perspective. We employ these concepts to set a research agenda on compound urban crises, highlighting multiple interconnections between urban politics and global dynamics. We conclude by suggesting how these entry points provide a theoretical anchor to develop practical insights to inform and reform urban governance.