With the rapid development of cloud computing, users are beginning to move their data to the cloud servers in order to avoid troublesome data management at local machines and enjoy convenient service. To protect data security and user privacy, data are usually stored in encrypted form in the cloud, but it activates the inconvenience when the user tries to retrieve the files containing some interested keywords. Searchable encryption (SE) is a recently developed cryptographic primitive that supports keyword search over encrypted data, which not only saves huge network bandwidth and computation capacity for users, but also migrates the cumbersome search operation to the cloud server to utilize its vast computational resources. This paper first introduces the research background and the current development of SE schemes and compares the different features between symmetric key cryptography based SE schemes and public key cryptography based SE schemes. The research status of the search query supported in SE schemes is then provided. The discussion includes the support of single keyword search query, conjunctive (and multi-keyword) search query and complex search query, respectively. Finally, this study presents the typical application scenario of SE schemes, and discusses the possible development tendency.