Hierarchy is a fundamental organizing principle of social life. Differences in rank power or status pervade nearly all social collectives, and they profoundly influence individuals, groups, and societies. Here we bring together the latest psychological science on the topic, complemented with insights from anthropology, sociology, biology, and management. At the intrapersonal level, we review research on the desire for social rank, its physiological and health correlates, its effects on affect, cognition, and behavior, and the perception, representation, and signaling of rank. At the interpersonal level, we discuss emerging insights into the social processes whereby individuals gain or lose rank, how rank shapes social sensitivity, emotional responsiveness, and morality, and how differences in rank shape cooperation, competition, and aggression. At the group level, we consider how differences in rank emerge in groups and organizations, and how such differences shape group dynamics. At the societal level, we explore the universality of rank asymmetries across cultures and stages of development and in the context of intergroup relations and economic inequality. We conclude by evaluating the current state of the science (including unresolved issues), offering heuristic definitions of key concepts, highlighting recent methodological advances, and calling for greater theoretical integration and interdisciplinary exchange.