  A vector database is used to store high-dimensional data that cannot be
characterized by traditional DBMS. Although there are not many articles
describing existing or introducing new vector database architectures, the
approximate nearest neighbor search problem behind vector databases has been
studied for a long time, and considerable related algorithmic articles can be
found in the literature. This article attempts to comprehensively review
relevant algorithms to provide a general understanding of this booming research
area. The basis of our framework categorises these studies by the approach of
solving ANNS problem, respectively hash-based, tree-based, graph-based and
quantization-based approaches. Then we present an overview of existing
challenges for vector databases. Lastly, we sketch how vector databases can be
combined with large language models and provide new possibilities.
