The rapid increase in consumption of products and services is leading to the scarcity of resources and environmental crisis. The circular economy was born as a new economic model to solve these problems. It explores new techniques to rethink and redesign products and services and extend their useful life through reusing, remanufacturing, recycling, etc., to maximize the value of resources. The implementation of the circular model entails the adaptation of supply chains. In connection with sustainability, we also need to consider economic, social and environmental dimensions. This makes the evaluation of the circular systems more complex. In the past, various means are presented in the literature to evaluate and understand the sustainable dimensions for the development of the circular economy. However, the evaluation methods and the indicators are heterogeneous. Thus, it is very challenging to obtain standardized information that the different stakeholders will understand. In this paper, through a literature review, we seek to understand the measurement of the sustainable dimensions in the performance of the circular supply chains. This research is part of a thesis work, which aims to study sustainable performance in circular supply chains, grouping economic, management and industrial engineering aspects.