The shift from a linear to a circular economy has the potential to simultaneously reduce uncertainties of material supplies and waste generation. To date, the development of robotic and, more generally, autonomous systems have been rarely integrated into circular economy implementation strategies. In this review, we merge deep-learning vision, compartmental dynamical thermodynamics, and robotic manipulation into a theoretically-coherent physics-based research framework to lay the foundations of circular flow designs of materials, and hence, to speed-up the transition from linearity to circularity. Then, we discuss opportunities for robotics in circular economy.