The pioneering efforts of Moscovici in the late 1960s motivated social psychologists to understand how minority groups affected the majority, and conversely, how the majority affected the minority. The underlying processes of influence have been found to be quite different, and understanding their operation provides insight into the processes of social influence, persuasion, and intragroup conflict and cooperation. This review tracks some of the development of this progression and details some contributions to understanding fundamental features of the influence process that have been uncovered as a result of this work. We consider major explanatory models, with particular emphasis on Crano's (2001) context/comparison model, and its allied leniency contract, a comprehensive account of the conditions that prevail when majorities and minorities wield influence. Finally, how this work informs important processes of influence in the world outside the laboratory are discussed.