Global economies have been characterised by a large dependency of material inflows from natural stocks, an exponential growth of material stock-in-use in the built environment, and the extensive disposal of waste material outflows to anthropogenic sinks. In this context, the concept of the circular economy has emerged, promising to circulate the stock-in-use of materials and transforming output waste material flows back into useful resources while promoting job and value creation. These promises have drawn the attention and interest of policymakers and industry, and gained popularity across society. Despite its apparent emergent legitimacy and diffusion, a few essential adjustments still need to be addressed so that circular economy initiatives can actually deliver on their promises without leading to negative unintended effects. First, a complete entanglement with the existing formal economy is fundamentally needed; this implies valuing the preservation of natural stocks and pricing material input flows adequately. Secondly, a recognition of its socio-economic embeddedness is essentially necessary. The decision-making of societal actors affects material configuration, which in turn affects societal actors; this important feedback loop needs to be explicitly taken into account in circular economy initiatives. The aim of this short communication paper is to explore these pervasive challenges in a broad context of sustainable physical resource management. An integrative framework for recognising the socio-economic embeddedness of the circular economy in practice and the role of the formal economic system in realising its ambitions is proposed.