Decarbonization of the electric power sector is essential for sustainable development. Low-carbon generation technologies, such as solar and wind energy, can replace the CO2-emitting energy sources (coal and natural gas plants). As a sustainable engineering practice, long-duration energy storage technologies must be employed to manage imbalances in the variable renewable energy supply and electricity demand. Compressed air energy storage (CAES) is an effective solution for balancing this mismatch and therefore is suitable for use in future electrical systems to achieve a high penetration of renewable energy generation. This study introduces recent progress in CAES, mainly advanced CAES, which is a clean energy technology that eliminates the use of fossil fuels, compared with two commercial CAES plants at Huntorf and McIntosh which are conventional ones utilizing fossil fuels. Advanced CAES include adiabatic CAES, isothermal CAES, liquid air energy storage, supercritical CAES, underwater CAES, and CAES coupled with other technologies. The principles and configurations of these advanced CAES technologies are briefly discussed and a comprehensive review of the state-of-the-art technologies is presented, including theoretical studies, experiments, demonstrations, and applications. The comparison and discussion of these CAES technologies are summarized with a focus on technical maturity, power sizing, storage capacity, operation pressure, round-trip efficiency, efficiency of the components, operation duration, and investment cost. Potential application trends were compiled. This paper presents a comprehensive reference for developing novel CAES systems and makes recommendations for future research and development to facilitate their application in several areas, ranging from fundamentals to applications.