Context: The environmental and social dimensions of performance are of great importance, given that they must be incorporated into strategic, tactical, and operational objectives in companies and supply chains to minimize negative impacts on the environment and society. Method: After reviewing the Scopus, Web of Science, and ScienceDirect databases for the topics of sustainability and supply chain management, a state of the art of green and sustainable supply chain management is presented, aiming to guide readers towards a synthesis of related concepts and future lines of research. Results: The reader is introduced to concepts and trends around the field of green and sustainable supply chain management to raise interest in new research and practices to guide the implementation of sustainability in organizations and their supply chains. Conclusions: Sustainable supply chain management still faces several academic and practical challenges in terms of implementation, performance measurement, and how models can capture a dynamic and uncertain social and environmental context. There are latent research issues such as management of the circular supply chain, applications in emerging economies, or the application of 4.0 technologies.