Complex systems are subject to changes that are nonlinear, commonly hard to anticipate, often abrupt, and sometimes transformative. In recent years, these phenomena have become a focus of considerable interest among natural scientists who speak about thresholds or boundaries (often characterized as tipping points), trigger mechanisms, and state changes. Similar phenomena occur in social systems involving shifts from peace to war and back, the collapse and replacement of political systems, and fluctuations between periods of economic growth and depression. In this context, it is helpful to differentiate among explosions, cascades, and inflections. The dynamics of such transitions are determined by the fragility of the relevant systems and the intensity of the trigger mechanisms. Building on analyses of tipping points and trigger mechanisms in biophysical systems and socioeconomic systems leads to a consideration of similar phenomena in socioecological systems of the sort that are central to the pursuit of sustainability in the Anthropocene. In considering the role of governance in such settings, it is important to bear in mind that governance systems, too, are complex and dynamic.