The underlying aim of this research is to investigate the mathematical descriptions of homogeneous textures in digital images for the purpose of segmentation and recognition. The research covers the problem of testing these mathematical descriptions by using them to generate synthetic realisations of the homogeneous texture for subjective and analytical comparisons with the source texture from which they were derived. The application of this research is in analysing satellite or airborne images of the Earth's surface. In particular, Synthetic Aperture Radar (SAR) images often exhibit regions of homogeneous texture, which if segmented, could facilitate terrain classification. In this thesis we present noncausal, nonparametric, multiscale, Markov random field (MRF) models for recognising and synthesising texture. The models have the ability to capture the characteristics of, and to synthesise, a wide variety of textures, varying from the highly structured to the stochastic. For texture synthesis, we introduce our own novel multiscale approach incorporating a new concept of local annealing. This allows us to use large neighbourhood systems to model complex natural textures with high order statistical characteristics. The new multiscale texture synthesis algorithm also produces synthetic textures with few, if any, phase discontinuities. The power of our modelling technique is evident in that only a small source image is required to synthesise representative examples of the source texture, even when the texture contains long-range characteristics. We also show how the high-dimensional model of the texture may be modelled with lower dimensional statistics without compromising the integrity of the representation. We then show how these models -- which are able to capture most of the unique characteristics of a texture -- can be for the ``open-ended'' problem of recognising textures embedded in a scene containing previously unseen textures. Whilst this technique was developed for the practical application of recognising different terrain types from Synthetic Aperture Radar (SAR) images, it has applications in other image processing tasks requiring texture recognition.