•This paper reviews practices and research in circular supply chain management.•Circular supply chain management is established as a multi-dimensional concept.•Five noticeable research-practice gaps are identified from the comparative review.•Eight promising research directions are discussed in circular supply chain management. The circular economy (CE) concept has gained wide attention in practice as well as in academia in recent years. This paper reviews the state-of-the-art practices and research in “circular supply chain management” (CSCM), i.e., the integration of CE thinking into supply chain management (SCM) with the goal of achieving “zero wastes”. The review covers 68 real-life CE implementation cases collected by the Ellen MacArthur Foundation and 124 publications in well-established, high-ranking academic journals in operations and supply chain management. The comparative review shows that CSCM encompasses multiple dimensions, including closed-loop SCM, reverse SCM, remanufacturing SCM, recycling SCM, and industrial symbiosis. A multi-dimensional CSCM (MD-CSCM) framework is developed to synthesize their interrelationships and to categorize academic publications into multiple research themes. Based on the identified research-practice gaps and pressing research needs, this study discusses important directions for future studies to advance supply chain circularity.