Enthusiasm for the Circular Economy (CE) is widespread and overwhelming. However, confusion around its meaning and purpose still pervades the scientific debate. Our study has two objectives. The first one is to increase the theoretical clarity and the scientific relevance of this debate. An important step forward in this direction is the idea of economy’s circularity, which we introduce following a critical re-visitation of CE’s notion. The second objective is to study the environmental effects of circularity. Our notion of economy’s circularity is theoretically rooted in the materials-energy balance model, and points to the presence of circular matter and energy flows in the economy. A major strength of this definition is the conceptual separation of circularity (as an economy’s feature) from the strategies (e.g. recovery, remanufacturing, reusing…) for its implementation. On one hand, this separation prompts the construction of a coherent framework, which helps shed light on the entire debate. On the other hand, it paves the way towards a novel methodology for studying any type of circularity effect. Circularity effects are indeed the effects of circularity strategies. Since strategies are constantly evolving, this approach delivers an immediate result. Circularity effects are unavoidably ambiguous. With reference to the effects on the environment, we provide evidence for this ambiguity by accurately selecting and reviewing studies on various circularity strategies. In a policy perspective, our findings seriously challenge the idea of implementing circularity for the sake of circularity. Indeed, using circularity as an environmental policy may prove quite a daunting task.