As an effective approach of implementing power load shifting, fostering the accommodation of renewable energy, such as the wind and solar generation, energy storage technique is playing an important role in the smart grid and energy internet. Compressed air energy storage (CAES) is a promising energy storage technology due to its cleanness, high efficiency, low cost, and long service life. This paper surveys state-of-the-art technologies of CAES, and makes endeavors to demonstrate the fundamental principles, classifications and operation modes of CAES. Critical subsystems of CAES are elaborated exhaustively. The application prospects and further research directions are summarized to promote the popularization of CAES in smart grid and energy internet.