Corporate greenhouse-gas emissions are attributed to global supply chains which represent a significant proportion of corporate greenhouse-gas emissions, especially indirect (Scope 3) emissions by upstream suppliers, logistics, manufacturing and raw-material sourcing. The paper provides a review of the key approaches firms are employing to minimize carbon footprints in global supply chains, examines the enablers and obstacles, and suggests a framework through which the decarbonization of the supply-chain operations can be embedded. Some of the major strategies are sustainable sourcing, optimization of logistics, circular economy, energy-efficient production, the implementation of renewable energy sources, the introduction of digital carbon-accounting and supplier partnerships. Based on the latest literature and industry examples, this paper gives an insight on the role of technology, governance and supply-chain design in making significant emission reductions, as well as pinpointing the implementation issues and future research opportunities.