This is a study of the growth and decline of cities for the purpose of identifying those events in which they significantly increased in size. Significant changes in the scale of cities are important for understanding the long-term trend toward more complex and hierarchical human societies. We report the results of an inventory of cycles, upsweeps, and collapses of settlements in five separate interpolity systems. Upsweeps are instances in which the largest settlement in a world system significantly increases in size. Collapses occur when the size of the largest settlement greatly decreases and stays down for a significant period of time rather than rebounding. We use regional interpolity systems (world systems) rather than single polities or settlements as our unit of analysis. Because the accurate designation of sweeps requires interval scale measures, we are limited to those regions and time periods for which quantitative estimates of largest settlement sizes are regularly available. We find a total of 18 upsweeps and five downsweeps, and only two instances of prolonged systemwide settlement collapse. We also investigate whether or not the rate of cycles has increased over the long run, and we find that cycles of city growth and decline have not accelerated. We also find a greater rate of urban cycles in the Western (Central) System than in the East Asian System, which supports the usual notion that the Western city system was less stable than the Eastern city system.