Many powerful computing technologies rely on implicit and explicit data contributions from the public. This dependency suggests a potential source of leverage for the public in its relationship with technology companies: by reducing, stopping, redirecting, or otherwise manipulating data contributions, the public can reduce the effectiveness of many lucrative technologies. In this paper, we synthesize emerging research that seeks to better understand and help people 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 change technology company behavior related to privacy, economic inequality, content moderation and other areas of societal concern. Our framework also points towards ways that policymakers can bolster data leverage as a means of changing the balance of power between the public and tech companies.