This thesis describes research conducted at City University into the application of Artificial Neural Networks (ANNs). ANNs have been evaluated as candidate solutions to two common tasks: classification and forecasting. More specifically the ANN models considered were those that could be implemented as computer algorithms suitable for the application domains considered. ANNs have emerged from a multi-disciplinary field of researchers attempting to understand and model biologically inspired neural systems on both the small and large scale. At the small end of the scale individual processing elements are studied in depth whilst in the large scale, networks containing many interconnected elements are simulated and behaviour analysed. The capabilities of the more mature ANN models have been explored in depth, with several being applied to domains, competing with established techniques such as machine learning, statistical methods and mathematical modelling. The relatively new field of ANN research is characterised by recent expansion in academic activity, rapid and widespread application of models and much debate over the benefits and performance of such models (not without controversy). The motivation behind this study was to evaluate objectively the potential of ANN models in what can be termed 'real world' problems, as opposed to artificial tasks based on synthetic data. Real, rather than artificial data were used in the applications presented, since one of the perceived benefits of ANN models is the ability to cope with the noisy, complex and often high dimensional data sets found in many 'real world' problem domains.