The Circular Economy is gaining traction in academia, industry, and policy making as an alternative model that minimises resource depletion, waste, and emissions. To implement the concept on the organisational level, business models are an important leverage. A body of literature has emerged investigating the notion of circular business model and circular business model innovation, however, there is considerable lack of clarity about their theoretical conceptualisation. To address this and systematise the state-of-the-art of the nascent field of circular business models and circular business model innovation, we have reviewed this literature, employing systematic database searches and cross-reference snowballing. Our contributions to conceptual clarity are: (1) an overview of the history of the concepts of circular business model and circular business model innovation, (2) an overview and synthesis of definitions of circular business model and circular business model innovation, and (3) an overview and synthesis of conceptual frameworks for circular business model and circular business model innovation. •Circular business models are key levers for the implementation of a circular economy.•There is still considerable lack of clarity about their theoretical conceptualisation.•History of the circular business model and circular business model innovation concepts.•Definitions for CBM and CBMI.•Conceptual frameworks for CBM and CBMI.