The processing power of the computer has increased at extraordinary rates over the last few decades. However, even today's fastest computer can take several hours to find solutions to some complex mathematical problems, and there are instances when a high powered supercomputer may be impractical, with the need for near instant solutions just as important. One approach to this kind of problem is through machine learning. This research investigates the application of various neural network techniques, and aims to solve known complex inverse problems in the field of magnetic and optical recording. Investigations were conducted to determine anisotropy distributions from transverse susceptibility data ( an area of magnetism which is proving to be very important, as it gives information about the overwrite characteristics of the media). The neural networks produced results which were very impressive, and compared well with other more conventional methods (solutions were obtained in a fraction of the time). More importantly, it suggested that this technique was indeed feasible, and could be used to solve a series of similar inverse problems. The neural network was then modified to investigate diffraction patterns from a compact disc. This was an interesting application which had practical uses in industry, as the idea of reducing the testing time for each disc was very attractive. Simulations on theoretical data were successful, and suggested that this method could be carried out experimentally on an online testing system. The final part of the research involved the extraction of important features from magnetisation maps and magnetic force microscopy images. The use of neural networks to study general image analysis is well established, but its use in magnetism was quite novel. The results obtained were surprisingly good as the images investigated hardly contained enough data for the human eye to observe, and features such as percolation and vortices were observed on a variety of samples. This success has prompted suggestions as to ways in which this approach can be expanded to solve similar problems.