Transitioning from the current linear economic development model to a circular economy (CE) is a hot topic in academic literature, public governance, and the corporate domain. Actors have implemented CE strategies to reduce their resource use and its associated impacts, while boosting economic competitiveness and generating positive social impact. Companies are identified as key actors in transitioning to a CE, and many academics have proposed tools to assess CE and guide them in this process. This paper critically reviews such academic ‘assessment approaches’ at the micro level in order to reflect on their key properties. Seventy-four approaches are inventoried through a systematic literature review of academic literature. A critical review framework is constructed and applied, containing four perspectives: A general perspective, a descriptive perspective (methodological aspects), a normative perspective (connections to Sustainable Development), and a prescriptive perspective (implementation-focused). Methodologically, the 74 approaches are highly diverse, having various connections to previously established methodologies. Eighteen of the reviewed assessment approaches include all three dimensions of Sustainable Development (SD), in addition to a ‘circular’ dimension. Roughly one quarter of the approaches apply a participatory design approach. Suggested key desired properties of CE assessment approaches include making use of existing assessment methodologies such as Life Cycle Assessment (LCA), and a closer collaboration between science and practitioners to consider end-user needs in the design of CE assessment approaches.