While sustainability is an essential concept to ensure the future of humanity and the integrity of the resources and ecosystems on which we depend, identifying a comprehensive yet realistic way to assess and enhance sustainability may be one of the most difficult challenges of our time. We review the primary environmental sustainability assessment approaches, categorizing them as either being design-based or those that employ computational frameworks and/or indicators. We also briefly review approaches used for assessing economic and social sustainability because sustainability necessitates integrating environmental, economic, and social elements. We identify the collective limitations of the existing assessment approaches, showing that there is not a consistent definition of sustainability, that the approaches are generally not comprehensive and are subject to unintended consequences, that there is little to no connection between bottom-up and top-down approaches, and that the field of sustainability is largely fragmented, with a range of academic disciplines and professional organizations pursuing similar goals, but without much formal coordination. We conclude by emphasizing the need for a comprehensive definition of sustainability (that integrates environmental, economic, and social aspects) with a unified system-of-systems approach that is causal, modular, tiered, and scalable, as well as new educational and organizational structures to improve systems-level interdisciplinary integration.