Human success in navigating the social world is typically attributed to our capacity to represent other minds—a mentalistic stance. We argue that humans are endowed with a second equally powerful intuitive theory: an institutional stance. In contrast to the mentalistic stance, which helps us predict and explain unconstrained behavior via unobservable mental states, the institutional stance interprets social interactions in terms of role-based structures that constrain and regulate behavior via rule-like behavioral expectations. We argue that this stance is supported by a generative grammar that builds structured models of social collectives, enabling people to rapidly infer, track, and manipulate the social world. The institutional stance emerges early in development and its precursors can be traced across social species, but its full-fledged generative capacity is uniquely human. Once in place, the ability to reason about institutional structures takes on a causal role, allowing people to create and modify social structures, supporting new forms of institutional life. Human social cognition is best understood as an interplay between a system for representing the unconstrained behavior of individuals in terms of minds and a system for representing the constrained behavior of social collectives in terms of institutional structures composed of interlocking sets of roles.