With the rapid development of the Internet and the penetration of big data mining and applications into all walks of life, how to share and use massive data securely and efficiently has become a new hot research issue. Secure multi-party computation is one of the key technologies to solve this problem. It allows a group of participants to interact compute a function together, and get the output without revealing private inputs. Oblivious transfer is a privacy-protected two-party communication protocol in which a sender holds two messages to be sent, and a receiver selects one to receive, but after that, the sender knows nothing about which message the receiver gets, and the receiver cannot get any information about the unselected message. Oblivious transfer has become one of the key modules of secure multi-party computation, and its efficiency optimization can effectively promote the application of secure multi-party computation, especially for special two-party secure computation protocols such as private set intersection. This paper summarizes the classification of oblivious transfer and several common variants, and respectively describes the construction and research progress of the oblivious transfer protocol based on public key cryptography and oblivious transfer extension, which leads to the importance of the efficiency optimization research of oblivious transfer. At the same time, this paper comprehensively reviews the research progress of efficiency optimization of oblivious transfer and oblivious transfer extension from the perspectives of semi-honest adversary and malicious adversary. On the other hand, in practical application, this paper systematically summarizes the optimization technologies used in the engineering implementation of oblivious transfer and oblivious transfer extension protocols. Finally, this paper points out the main problems and future works of oblivious transfer and oblivious transfer extension protocols.