Carbon capture and storage is expected to play a pivotal role in achieving the emission reduction targets established by the Paris Agreement. However, the most mature technologies have been shown to reduce the net efficiency of fossil fuel-fired power plants by at least 7% points, increasing the electricity cost. Carbonate looping is a technology that may reduce these efficiency and economic penalties. Its maturity has increased significantly over the past twenty years, mostly due to development of novel process configurations and sorbents for improved process performance. This review provides a comprehensive overview of the calcium looping concepts and statistically evaluates their techno-economic feasibility. It has been shown that the most commonly reported figures for the efficiency penalty associated with calcium looping retrofits were between 6 and 8% points. Furthermore, the calcium-looping-based coal-fired power plants and sorption-enhanced hydrogen production systems integrated with combined cycles and/or fuel cells have been shown to achieve net efficiencies as high as 40% and 50–60%, respectively. Importantly, the performance of both retrofit and greenfield scenarios can be further improved by increasing the degree of heat integration, as well as using advanced power cycles and enhanced sorbents. The assessment of the economic feasibility of calcium looping concepts has indicated that the cost of carbon dioxide avoided will be between 10 and 30 € per tonne of carbon dioxide and 10–50 € per tonne of carbon dioxide in the retrofit and greenfield scenarios, respectively. However, limited economic data have been presented in the current literature for the thermodynamic performance of calcium looping concepts.