This paper reviews previous research on the two basic searchable encryption problems, and introduces the classification of searchable encryption (SE), including its application scenarios and usage models. After discussing the resolution strategies, it divides SE into two groups, that is symmetric searchable encryption and asymmetric searchable encryption. Based on this classification, the research advance is surveyed on basic definition, typical construction and extended research. Finally, the need-to-be-solved problems and main research directions are discussed. This study aims at promoting further research of searchable encryption.