Image compression utilises data redundancy to generate a reduced data representation from which the original image can be reconstructed with the introduction of only small coding errors. Data compression reduces the storage or transmission bandwidth required by the application. In the development of compression methods the aim is to minimise the coding error while increasing the compression ratio. Also, the complexity of the coding algorithm must be considered if a cost-effective solution is being sought. This thesis reviews the current status of image compression and identifies Vector Quantization (VQ) as a technique which provides good compression and error performance whilst retaining an essentially simple structure which is suitable for VLSI implementation. The coding performance that can be obtained with VQ is extremely sensitive to the quality of the codebook, which is very specific to the training data used to generate it. A novel codebook generation method is presented here which uses intelligent techniques to ensure that the codebook is effectively populated with a wide range of vector types for optimal coding performance. This thesis also investigates the use of VQ for coding image sequences. Two separate techniques, developed by the author, which code image sequences without adapting the codebook over time, are presented. The performance of these techniques is fundamentally limited and the need for codebook adaptation is clear. The aim of codebook adaptation is to maintain a codebook which remains effective as the image content changes, whilst adding a minimum data and processing overhead. Methods for codebook adaptation are analysed through experiment and provide a codebook adaptation technique which is effective, whilst being efficient in bit-rate terms and incurring little additional processing costs.