In this Chapter we show that by considering eye movements, and in particular, the resulting sequence of gaze shifts, a stochastic process, a wide variety of tools become available for analyses and modelling beyond conventional statistical methods. Such tools encompass random walk analyses and more complex techniques borrowed from the pattern recognition and machine learning fields... After a brief, though critical, probabilistic tour of current computational models of eye movements and visual attention, we lay down the basis for gaze shift pattern analysis. To this end, the concepts of Markov Processes, the Wiener process and related random walks within the Gaussian framework of the Central Limit Theorem will be introduced. Then, we will deliberately violate fundamental assumptions of the Central Limit Theorem to elicit a larger perspective, rooted in statistical physics, for analysing and modelling eye movements in terms of anomalous, non-Gaussian, random walks and modern foraging theory. Eventually, by resorting to machine learning techniques, we discuss how the analyses of movement patterns can develop into the inference of hidden patterns of the mind: inferring the observer's task, assessing cognitive impairments, classifying expertise. (read more)