A finite-state vector quantizer is a finite-state machine used for data compression: Each successive source vector is encoded into a codeword using a minimum distortion rule, and into a code book, depending on the encoder state. The current state and the selected codeword then determine the next encoder state. A finite-state vector quantizer is capable of making better use of the memory in a source than is an ordinary memoryless vector quantizer of the same dimension or blocklength. Design techniques are introduced for finite-state vector quantizers that combine ad hoc algorithms with an algorithm for the design of memoryless vector quantizers. Finite-state vector quantizers are designed and simulated for Gauss-Markov sources and sampled speech data, and the resulting performance and storage requirements are compared with ordinary memoryless vector quantization.