This paper investigates a puzzling feature of social conventions: the fact that they are both arbitrary and normative. We examine how this tension is addressed in sociological accounts of conventional phenomena. Traditional approaches tend to generate either synchronic accounts that fail to consider the arbitrariness of conventions, or diachronic accounts that miss central aspects of their normativity. As a remedy, we propose a processual conception that considers conventions as both the outcome and material cause of much human activity. This conceptualization, which borrows from the économie des conventions as well as critical realism, provides a novel perspective on how conventions are nested and defined, and on how they are established, maintained and challenged.