With the continuous development of big data and cloud computing technology， cloud platforms have become the first choice for massive data storage， and user data privacy and security has become one of the most important issues in cloud computing environment. In order to ensure security of data， users usually encrypt sensitive data and then store it in cloud servers. And how to efficiently retrieve ciphertext data on the cloud becomes a challenge. Searchable encryption technology provides an effective method for solving efficient retrieval of ciphertext by allowing users to directly retrieve ciphertext data through keywords， which protects data privacy while reducing communication and computing overhead. In recent years， in order to cope with different platforms and application scenarios， Public-key Encryption with Keyword Search （PEKS） technology has produced a large number of extension schemes based on different difficult problems， query methods， and changing structures. For security extensions and functional extensions， PEKS extension schemes were reviewed in terms of permission sharing， key management issues， fine-grained search and access control capabilities of current application requirements， and the performance of the specifically described solutions were compared and analyzed in depth， pointing out the advantages and shortcomings. Finally， the development trends of PEKS technology was summarized and prospected.