Abstract: With the rapid development of cloud computing, quantum computing and other advanced technologies, data privacy is facing increasingly severe threats. Especially in recent years, more and more users have been storing their sensitive data and applications in the cloud to take advantage of convenient services and powerful computing capabilities. However, traditional security technologies can not fully guarantee the security of cloud computing. Introducing fully homomorphic encryption algorithms is one of the effective ways to address this issue. At the same time, fully homomorphic encryption technology based on lattice theory has the capabilities of natural resistance to quantum attacks and arbitrary calculations on data in an encrypted state, effectively guaranteeing data security in the quantum computing era. Although fully homomorphic encryption shows significant potential, it suffers the problem of the volume explosion of computing and storage. To address the above problem and speed up the widespread adoption of fully homomorphic encryption algorithms, researchers from the fields of algorithms and hardware have been proposed a variety of solutions, and significant progress has been made. This work summarizes the progress of mainstream fully homomorphic encryption technology, analysis and compilation of algorithm libraries and fully homomorphic hardware accelerator in the past five years, and finally provides perspective of fully homomorphic encryption technology future development.