Widespread adoption of sustainable and circular business models is required to accelerate the transition to a more sustainable society, however, the literature supporting the process of Business Model Innovation for the Circular Economy - or Circular Business Model Innovation (CBMI) - is currently emerging. Several publications on this field have been published since 2014, nevertheless, there is still a lack of understanding on the process of CBMI, particularly for incumbent firms; and, as most of the literature is theoretical, further empirical insights are required. Furthermore, there is a need for an updated and comprehensive review of this fast-paced field, and a need to further integrate the CBMI field with the conventional Business Model Innovation (BMI) domain. The present research aims to first, map and frame the field of CBMI, building upon the structure of the conventional BMI field; second, to assess the current state of research of the field, proposing a future research agenda; and third, to explore the most relevant elements of the CBMI process in the practice. The article uses a combined literature and multiple case study approach. It begins by synthesizing a BMI framework, which is then combined with the findings of a systematic literature review (n=84) on the emergent CBMI field, to propose an original framework that structures the field. The review includes an assessment per article on the state-of-research. The framework is then illustrated through a multiple case study on ten incumbent firms that have implemented a substantial CBMI, revealing which topics are more relevant from a practice perspective and offering valuable empirical insights. We suggest that future research should prioritize those topics that are very important from the practice and still un- or under-researched in the CBMI field (i.e. organizational culture and structure as moderators of the CBMI change process, sustainability strategy as an antecedent of CBMI and top management role as key elements of the CBMI process) and to those identified as important though under-researched (i.e. organizational change management as a key element of the CBMI process; organizational inertia, ambidexterity and CBMI uncertainties as moderators of the CBMI process; and systemic change as an effect of the CBMI). The literature on Sustainable BMI is integrated to propose contributions to the identified gaps. This research contributes by framing and assessing the field of CBMI, proposing a future research agenda, providing a detailed literature state-of-research assessment and by further integrating CBMI with the conventional BMI field.