Fully Homomorphic Encryption(FHE)is a multi-party secure computation protocol characterized by its high computational complexity and low interaction requirements.Although there is no need for multiple rounds of interactions and extensive communications between computing participants in protocols based on FHE,the processing time of encrypted data is typically 103 to 106 times of that of plaintext computing,and thus significantly hinders the practical deployment of such protocols.In particular,the large-scale darallel cryptographic operations and the cost of data movement for the ciphertext and key data needed in the operations become the dominating performance bottlenecks.The topic of accelerating FHE in both the software and the hardware layers is discussed in this paper.By systematically categorizing and organizing existing literatures,a survey on the current status and outlook of the research on FHE is presented.