As an effective strategy to implement electrical load shifting and to encourage the use of alternative renewable energies, such as solar and wind generation, the energy storage system plays an important role in the energy internet and the smart grid. Compressed air energy storage is a promising technique due to its efficiency, cleanliness, long life, and low cost. This paper reviews CAES technologies and seeks to demonstrate CAES's models, fundamentals, operating modes, and classifications. Application perspectives are described to promote the popularisation of CAES in the energy internet and smart grids. We review recent work on CAES. We evaluate and analyse these results to discover gaps and opportunities. The most important results indicate that CAES is generally considered an EES (electrical energy storage) option for wind power integration. However, current research is beginning to investigate CAES in combination with solar energy systems. Gaps may be identified in the study associated with CAES for microgrid integration and demand management which are future uses of CAES.