Modelling of spatially homogeneous and piecewise-homogeneous image textures by novel Markov and non-Markov Gibbs random fields with multiple pairwise pixel interactions is briefly overviewed. These models allow for learning both the structure and strengths (Gibbs potentials) of the interactions from a given training sample. The learning is based on first analytic and then stochastic approximation of the maximum likelihood estimates (MLE) of the potentials. A novel learning approach, giving explicit, to scaling factors, estimates of the potentials, is outlined. It exploits the conditional MLE provided that the training sample may rank a feasible top place within the parent population in its total Gibbs energy. The models embed both simulation and segmentation of the grayscale piecewise-homogeneous textures into the same Bayesian framework exploiting a controllable simulated annealing to generate the desired texture or its region map. Experimental results in simulating and segmenting various natural textures are presented and discussed.