Cloud computing facilitates convenient and on-demand network access to a centralized pool of resources. Currently, many users prefer to outsource data to the cloud in order to mitigate the burden of local storage. However, storing sensitive data on remote servers poses privacy challenges and is currently a source of concern. SE (Searchable Encryption) is a positive way to protect users sensitive data, while preserving search ability on the server side. SE allows the server to search encrypted data without leaking information in plaintext data. The two main branches of SE are SSE (Searchable Symmetric Encryption) and PEKS (Public key Encryption with Keyword Search). SSE allows only private key holders to produce ciphertexts and to create trapdoors for search, whereas PEKS enables a number of users who know the public key to produce ciphertexts but allows only the private key holder to create trapdoors. This article surveys the two main techniques of SE: SSE and PEKS. Different SE schemes are categorized and compared in terms of functionality, efficiency, and security. Moreover, we point out some valuable directions for future work on SE schemes.