Circular economy is an alternative to the traditional production model and has therefore attracted a great deal of attention from researchers. The change in the production system is accompanied by new logistical needs related both to resources and waste and to the distribution and recovery of products. The circular supply chain involves return processes and the manufacturer intends to capture additional value in the supply chain. In this paper, value chains have been mapped to visualize the links and interactions between the different stages and actors to understand the complexities of these systems and to make informed decisions. For this reason, and based on thorough literature review, the final objective of this work is to achieve a conceptual framework to study circular supply chain, which uses the main theoretical perspectives in strategic management literature. Four dimensions have been identified to support the development of these new supply chains—greater intensity in the relationships established in the supply chain, adaptation of logistics and organizational, disruptive and smart technologies, and a functioning environment. It can be concluded that to develop a new relationship capacity will allow for reaching more frequent, closer relationships with more actors. These relationships will be developed within an adapted organizational and logistical framework that is framed in new business model archetypes. However, dimensions related to the business environment such as sectoral, legislative, and fiscal frameworks must be incorporated.