With the advent of the big data era, the size and complexity of data continue to increase, which makes the requirement for data privacy and security increasingly urgent. However, traditional encryption methods cannot meet the demand for efficient searching in large-scale datasets. To solve this problem and enable users to search within encryped data and without decrypting the entire dataset, trapdoor functions and other cryptograhic techniques are introduced in searchable encryption. However, searchable encryption still cannot meet the needs in the real world. Therefore, researchers have introduced the concept of attribute-based encryption into searchable encryption, resulting in attribute-based searchable encryption (ABSE). This approach aims to achieve efficient search by attributes in encrypted datasets. ABSE has a wide range of applications in the fields of privacy protection, data sharing, and cloud computing. In this paper, we describe the trends in development, focusing on enhancing security, improving computational efficiency, and increasing flexibility. We also present the related schemes. In addition, several common application areas are introduced and the relevant schemes proposed by researchers are summarized. Moreover, the challenges and future directions of ABSE are discussed in this paper.