Many powerful computing technologies rely on data contributions from the public. This dependency suggests a potential source of leverage: by reducing, stopping, redirecting, or otherwise manipulating data contributions, people can influence and impact the effectiveness of these technologies. In this paper, we synthesize emerging research that helps people better understand and action this data leverage. Drawing on prior work in areas including machine learning, human-computer interaction, and fairness and accountability in computing, we present a framework for understanding data leverage that highlights new opportunities to empower the public in its relationships with technology companies. Our framework also points towards ways that policymakers can augment data leverage as a means of changing the balance of power between the public and tech companies. CCS CONCEPTS• Human-centered computing → Collaborative and social computing theory, concepts and paradigms.