High-dimensional approximate nearest neighbor search (ANNS) is one of the fundamental and core components of vector databases. With the advancement of artificial intelligence, vector databases have played an increasingly critical role and have gained widespread attention. ANNS methods are essential for optimizing the performance of vector databases. Over decades of development, ANNS has achieved a series of milestones. Rapid advancements in this field in recent years have led to a surge of novel methods and findings, necessitating systematic organization. In this study, the basic concepts of ANNS are first introduced. Next, building upon existing survey frameworks, current approaches are further categorized into five groups based on vector data organization methods: graph-based, hierarchical, quantization-based, hashing-based, and hybrid data organization. Representative works and the latest research advances in the field are systematically discussed. Then, from the perspective of vector search optimization methods, recent advancements are reviewed and categorized into eight types. These categories include hardware acceleration oriented, learning enhanced, distance comparison operation oriented, disk-memory hybrid oriented, data access optimization oriented, distributed oriented, hybrid query oriented, and theoretical analysis. Finally, based on current research achievements and trends, potential future research directions are outlined.