Abstract: With the acceleration of the digitization process, the problem of data security and privacy protection has attracted much attention. Data encryption has always been an important means to solve this problem. However, it is common to store and transfer data in encrypted form. Once calculation is involved, it is often necessary to decrypt the ciphertext, perform the calculation in plaintext, and then encrypt the calculation result. Full homomorphic encryption (FHE) extends encryption to the computing, which can perform meaningful calculations in ciphertext without decryption, and the calculation process and result are encrypted, so it has the natural characteristics of protecting data security and user privacy. The first FHE scheme was proposed by Gentry in 2009, and then FHE has always attracted the attention of the industry and academia. After more than ten years of research, FHE has developed to the fourth stage, and substantial progress has been made. We review and analyze the research progress of FHE from the aspects of the construction idea, different research stages and problems faced, introduce the application progress of FHE from the aspects of algorithm library, standardization progress and typical application scenarios, and put forward suggestions for future research direction.