As high-dimensional vector data increasingly surpasses the processing capabilities of traditional database management systems, Vector Databases (VDBs) have emerged and become tightly integrated with large language models, being widely applied in modern artificial intelligence systems. However, existing research has primarily focused on underlying technologies such as approximate nearest neighbor search, with relatively few studies providing a systematic architectural-level review of VDBs or analyzing how these core technologies collectively support the overall capacity of VDBs. This survey aims to offer a comprehensive overview of the core designs and algorithms of VDBs, establishing a holistic understanding of this rapidly evolving field. First, we systematically review the key technologies and design principles of VDBs from the two core dimensions of storage and retrieval, tracing their technological evolution. Next, we conduct an in-depth comparison of several mainstream VDB architectures, summarizing their strengths, limitations, and typical application scenarios. Finally, we explore emerging directions for integrating VDBs with large language models, including open research challenges and trends such as novel indexing strategies. This survey serves as a systematic reference guide for researchers and practitioners, helping readers quickly grasp the technological landscape and development trends in the field of vector databases, and promoting further innovation in both theoretical and applied aspects.