The aim of proposed research is to study various models of non-Markovian random walks modeling the dynamical properties of disordered media. Among these models, the focus is on random walks in random environments, random walks on random graphs like percolation clusters or random trees, reinforced random walks, and random walks in random sceneries. These models have different origins and motivations, but all have natural applications in physics, biology or engineering (see for instance [AH], [BDG], [BTDA], [CM], [dG], [MM], [lD], [St], ...) . All of these models exhibit strong dependence on the past, either by definition of the model itself, or as a consequence of averaging with respect to the random environment. This feature leads to a number of interesting questions, about recurrence/transience of these processes, limit theorems, or large deviations properties that we wish to address in the present project.