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 garnered widespread attention. ANNS methods are essential for optimizing the performance of vector databases. Over decades of development, ANNS has achieved a series of milestones and inspired many comprehensive surveys. Rapid advancements in this field in recent years have led to a surge of novel methods and findings, necessitating systematic organization. In this survey, we first introduce the basic concepts of ANNS. Next, building upon existing survey frameworks, we further categorize current approaches 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, we propose a classification system consisting of eight categories: hardware acceleration-oriented, learning-oriented, distance comparison operation-oriented, disk-oriented, data layout-oriented, distributed-oriented, hybrid query-oriented, and theoretical analysis, to review recent search achievements. Finally, based on current research achievements and trends, we outline potential future research directions.