Despite companies face several challenges when redesigning their supply chain for the Circular Economy, current literature lacks a systematisation of such challenges and of the ways to overcome them. Through a systematic literature review, this paper identifies and identifies 24 challenges that may hamper a supply chain redesign for the Circular Economy. Sixteen of these challenges are well known from research in related topics. On the other hand, the remaining eight are relatively new or take on a different relevance within the Circular Economy context. A multiple case study in the household appliance supply chain has been carried out to explore how these challenges appear in practice and how companies may tackle them. The cases analysed involve actors at different supply chain levels, and findings suggest that a great degree of vertical integration by one actor in the supply chain is not a necessary condition for Circular Economy implementation. The empirical study, in conjunction with the literature analysis, leads to the development of a framework linking the challenges to specific levers that companies may pursue to overcome them. The framework can be seen as a reference for managers taking the path towards a Circular Economy.