Vector quantization (VQ) is a very effective way to save bandwidth and storage for speech coding and image coding. Traditional vector quantization methods can be divided into mainly seven types, tree-structured VQ, direct sum VQ, Cartesian product VQ, lattice VQ, classified VQ, feedback VQ, and fuzzy VQ, according to their codebook generation procedures. Over the past decade, quantization-based approximate nearest neighbor (ANN) search has been developing very fast and many methods have emerged for searching images with binary codes in the memory for large-scale datasets. Their most impressive characteristics are the use of multiple codebooks. This leads to the appearance of two kinds of codebook: the linear combination codebook and the joint codebook. This may be a trend for the future. However, these methods are just finding a balance among speed, accuracy, and memory consumption for ANN search, and sometimes one of these three suffers. So, finding a vector quantization method that can strike a balance between speed and accuracy and consume moderately sized memory, is still a problem requiring study.