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This thesis investigates areas of neural networks and their application to aspects of image processing. Three neural network models, namely the backpropagation network, the Hopfield network and the competitive network, are studied. First, the learning algorithms for backpropagation networks and competitive neural networks are studied and new algorithms are developed. The applications of Hopfield neural networks to image coding, and of backpropagation networks to image data compression, are then investigated, and new techniques are presented. The learning algorithms for feed-forward neural networks are studied. A modified backpropagation algorithm is developed for accelerating the learning of backpropagation networks. Simulation results for four benchmark tasks are presented which show that the new method provides improved acceleration of learning, and global convergence characteristics. The learning algorithms for competitive neural networks are investigated. By incorporating principles of statistical mechanics into competitive learning, a new simulated annealing procedure for training competitive neural networks, the Stochastic Competitive Learning Algorithm (SCLA), is developed. Simulation results are presented which show that the SCLA is insensitive to the initial values of weight vectors, and can achieve a lower cost function value than other established competitive learning algorithms, and is therefore a valuable tool for data clustering. The computational power of Hopfield neural networks is employed for image coding applications. A new Hopfield neural network based block truncation coding (HNNBTC) technique is developed. The new HNNBTC is shown to provide improved performance over established block truncation coding techniques both in terms of mean square error performance and visual quality of the coded images. Two variations of the HNNBTC technique are also presented which are shown to provide increased compression ratios without sacrificing much of the visual quality of the coded images. The application of backpropagation networks to image data compression are investigated, and two new techniques are developed. The ceniralised MLP (CMLP) image data compression scheme is developed, which is aimed at improving the networks' generalisation capabilities, thereby enabling them to effectively compress a wide range of novel images. The learning edge patterns using MLPs (LEPMLPs) scheme, for image data compression is developed, which is aimed at improving the reconstruction of edges, thus improving the visual quality of the reconstructed images. Tabulated experimental results and example reconstructed novel images, for the original method and the new techniques, are presented, which demonstrate the improved image compression perfonnance gained using these new techniques.