How do economic agents manage anticipated shifts in regimes? How do they try to influence or prevent the arrival of such shifts? This paper provides a selective survey of the analysis of regime shifts from an economic viewpoint, with particular emphasis on the use of the techniques of optimal control theory and differential games. We examine the concepts of regime shifts, thresholds, and tipping points in both deterministic and stochastic settings, with or without ambiguity-aversion. Applications to the analysis of political regime shifts are reviewed, with a focus on the role of policy instruments such as repression, redistribution, and gradual democratization. Other dynamic games involving regime shifts that we survey include games of resource exploitation and games in industrial organization theory (R&D races, sabotage against rivals to prevent entry). We compare regime shifts under a Big Push and gradual regime changes.