Data security and privacy requirements are becoming more urgent as citizens use information technology in all aspects of life. Traditional encryption methods have been used to restrict data privacy, but searching for encrypted data has become an obstacle to retrieving it. This dilemma of searching encrypted data by citizens without decrypting the data has been solved through several searchable symmetric encryption (SSE) functions represented by single-keyword search, multi-keyword search, similarity/fuzzy search, ranking search, semantic search, dynamic SSE, and verifiable function. This review describes each scheme in terms of the idea, the data structure used, supporting function, performance, efficiency, and illustrative figures. In addition, we present a multi-function SSE scheme. Moreover, this work provides a table with a timeline summarizing all the schemes we discussed in this survey. This table is important and useful for researchers as it summarizes approximately 80 state-of-the-art works that cover the most important basic works published in popular indexes. Finally, the research gap in terms of privacy in encrypted data search schemes has been clarified.