The factors that make a society sustainable, or vulnerable to collapse, can rarely be discerned within a human lifetime. Sustainability challenges develop over periods of decades, generations, or centuries. Sustainability must therefore be a historical science. A major challenge of the IHOPE program is how to draw valid comparisons among different kinds of societies, existing at different times, that can clarify our contemporary problems of sustainability. This paper develops and illustrates a theory for understanding sustainability and collapse that has cross‐cultural applicability. Illustrating the theory by the collapse of the Western Roman Empire yields new insights into what it means to be a sustainable society. Comparison to the Maya reveals that, despite many differences, the Roman Empire and Maya polities underwent similar patterns of cultural evolution, and developed similar vulnerabilities. Comparison of both historical cases to the sustainability challenges of today demonstrates that contemporary industrial societies face evolutionary processes similar to those experienced by the Romans and the Maya. This analysis yields several points that are worthwhile for policy makers to understand.