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Punctuated equilibrium is regarded as the state of natural and social systems manifested in occasional intense, quick bursts of activity. Within the framework of the theory of self-organized criticality (SOC), punctuated equilibrium can be formalized as pink noise. SOC theory, having been developed by the end of 1980s, was originally intended to explain natural science phenomena. However, soon after its presentation, it began to spread across the social and humanitarian field of knowledge. Critical state is one on the brink of a bifurcation point. It turns out that some systems can stay in a state of permanent choice for a fairly long time. The author presents the examples of punctuated equilibrium revealed in computer experiments with artificial societies, as well as through empirical observation (particularly, in the dynamics of voting patterns, internet activity, and protest movements in the past and present). The key concepts of SOC theory and tools for pink noise identification are laid out. The sandpile model has been given special attention. Certain papers have been analyzed in which SOC theory was applied to gain some political science knowledge. According to SOC, in certain cases, there is no need to search for some significant extraordinary factor to shed light on explosive social transformations (including revolutions and other bursts of social and political activity). Social transformations can be induced by quite ordinary - and thus undistinguished - properties of systems, micro-level pro- cesses, and local impulses. SOC theory, therefore, refocuses the attention of researchers from the search for direct causes of events to the identification of states of the subject that generates these events.