Change in complex systems, system evolution, is itself complex. This paper is about world system evolution as it is reflected in the pattern of urbanization over the last 5000 years. It will be shown that the pattern of urbanization as part of the immensely complex world system exhibits non-linearity in that it is neither smooth nor continuous but rather is punctuated by periods of rapid change interspersed between periods of stasis. This pattern was first described in biological systems by Eldridge and Gould (1972) for speciation, and much of the pattern of urbanization reflects the characteristics of punctuated equilibrium first described by those two authors. Specifically, this paper will investigate the phenomenon of punctuated equilibrium reflected in both the macro-pattern of urbanization over historic time, i.e. the evidence for punctuated equilibrium as reflected by data on urbanization and on the level of state development, and possible mechanisms for such punctuated behavior including the general model of self-organized criticality as developed by Per Bak (1996), the role of hypercycle formation in punctuated equilibrium, the role of aromorphic processes, and the interaction between population, carrying capacity, and level of technology as represented by a very general math model.