Companies are involved in a context that involves fierce competitiveness, globalisation and worldwide requirements, including environmental care. This means that they must consider strategies to make their supply chains more sustainable in their operations planning. Therefore, this study proposes addressing the dimensions and challenges that companies must address to design their supply chains within the circular economy framework. For this reason, a conceptual framework design methodology is used, and this article addresses the visualisation, analysis and conceptualisation phases as a fundamental basis for subsequently planning the modelling, validation and proposal to define a conceptual model for the design of operations strategies in sustainable global supply chains in line with circular economy criteria. The obtained results show that the main dimensions considered by experts are: political, economic, social, technological, legal and environmental. The challenges to which these dimensions are exposed are cost, agility, flexibility, sustainability, resilience and digitisation.