A circular economy is an economic system aimed at maximizing resource efficiency while minimizing waste generation. Industry 4.0 and 5.0 concepts represent significant shifts in the industrial landscape driven by technological advancements and human-centric thinking. This paper reviews the literature on Industry 4.0/5.0 (I4.0/I5.0), Circular Economy (CE) and their relationship within a maturity model (MM). For this purpose, we compiled the most relevant maturity models for Industry 4.0/5.0 and Circular Economy. A systematic literature review, in conjunction with a descriptive analysis, was carried out to identify, select, and evaluate relevant articles. Trends and gaps have been identified. Findings highlights a need to explore the existing maturity models and to enhance the integration of circular economy in these MMs. The review outlines the research key areas that warrant attention to advance this field. This study concludes with a summary of research gaps, limitations and future research guidelines. Overall, we will contribute via this study towards the implementation of a coherent maturity model that enhance circular economy within an industry 4.0/5.0 area.