Abstract: With the development of Internet of things and big data technology, increasing distributed applications are booming in the personal computers and mobile phones. However, the existing distributed data processing methods have not met the needs of privacy protection. As a typical privacy-preserving technology for distributed set computation, private set intersection (PSI) protocols allow the participants to input individual sets and jointly calculate the intersection of these sets without disclosing any information except the intersection. As an important application of secure multiparty computation, PSI protocols have been widely used in privacy-preserving computation, which has theoretical and practical significance. Many PSI protocols have been emerged, but due to the lack of related surveys on PSI, we have written this paper. This paper introduces the fundamentals of PSI protocols such as the cryptographic technology, adversary model, security proof and implementation framework. And then the paper systematically summarizes the cryptographic framework of traditional PSI protocol from three aspects: the framework based on public key cryptosystem, garbled circuit, and oblivious transfer. Some of the key technologies in the set element comparison are introduced such as oblivious pseudo-random function, oblivious polynomial evaluation, and Bloom filter. Furthermore, a few of emerging PSI application scenarios are described in detail such as cloud-based PSI, unbalanced PSI, threshold PSI, and multiparty PSI. Finally, the paper summarizes the problems to be solved and prospects some possible development directions of PSI.