This paper investigates the recent progress of Locality-sensitive hashing (LSH) under different metrics and its adaptive performance in different application scenarios. LSH is an approximate nearest neighbor query algorithm, which aims to perform fast similarity finding in high-dimensional space. In recent years, the improvement directions of LSH can be divided into three categories: 1) constructing suitable function families under different metric indexes, 2) constructing detection sequences by perturbation, and 3) expanding the radius to improve the retrieval range. Since metric indexing is more widely used, this paper focuses on a comprehensive and schematic review of this approach. computational simplicity and efficiency of LSH, which is prominent in the fields of image, recommendation, and de-duplication, we review the latest research on LSH in different application scenarios to provide an advanced general framework and a better understanding of LSH in combination with other fields. In conclusion, various algorithms for LSH are evolving rapidly, and it is expected to see more diverse application scenarios for these methods in the future.