The COVID-19 pandemic revealed weaknesses in the global supply chain management. With stock-outs, transportation problems and the bullwhip effect caused by ever-changing demand, it is necessary for decision-makers to review their supply chain configuration. The latter must adapt to new market changes and respond quickly and cost-effectively to customer requirements. In fact, the selection criteria of the most reconfigurable configuration, i.e., the configuration that adapts its structure and its functions to the new market changes, must respond to this problem. The aim of this paper is to conduct a literature review of the criteria and methods for configuration selection in reconfigurable manufacturing systems and reconfigurable supply chains. This study allows to define a roadmap for the configuration selection in reconfigurable supply chains based on the most efficient reconfigurability criteria. We provide new trends to consider in this selection problem. This paper allows managers to choose the most appropriate criteria to implement a reconfigurable supply chain.