Circular economy (CE) is a sustainable alternative to tackle global challenges like climate change, waste, and pollution. The relations, perceptions and behaviors of stakeholders in circular economic activities may form barriers that hinder the circular transition. The promotion of CE requires investigating the interactions and information flow between CE stakeholders from a network perspective. This study revisits the applications of social network analysis (SNA) in promoting CE. Related concepts of CE and the research contents of SNA are reviewed. A bibliometric analysis is conducted to provide a bird’s eye on the research status and trend. On this basis, we summarize the challenges of promoting CE and refine specific problems, around which we review the research status of network modeling methods and statistical measures, information diffusion models, mining methods of perceptions, and social influence analysis. This study outlines the pathways through which SNA contributes to promoting CE, such as through revealing the relational structure and characteristics of stakeholders, forming and changing perceptions of stakeholders, improving behaviors of stakeholders, and examining the development of CE. The lessons learned from the review and future prospects are extensively discussed in combination with the features of the information age from both theoretical and practical perspectives.