The private set intersection (PSI) is a specific application problem that belongs to the field of secure multi-party computation. It not only has important theoretical significance but also has many application scenarios. In the era of big data, the research on this problem is in accord with people’s increasing privacy preserving demands at the same time to enjoy a variety of services. This paper briefly introduces the basic theory of secure multi-party computation, and highlights the two categories of current mainstream research methods of PSI under the framework of secure multi-party computation: the traditional PSI protocols based on the public key encryption mechanism, garbled circuit, oblivious transfer and the outsourced PSI protocols based on the untrusted third party service provider. Besides, we have briefly summarized the characteristic, applicability and complexity of those protocols. At the same time, the application scenarios of privacy preserving set intersection problem are also explained in detail, which further reflects the practical research value of the problem. With the deep research on the PSI problem, researchers have designed a set of private protocols that can quickly complete set intersection of millions of elements in the semi-honest model.