Abstract: Classical random walks have been studied for many decades, and by now detailed knowledge exists on almost every aspect of them. Not surprisingly, most of the methods for studying them are based on the regularity and group structure of the medium, as well as the Markovian behavior of the walk. However, when attempting to use random walk as a model for physical processes, both the assumption of regularity and that of Markovian behavior are no longer valid. Therefore in the last three decades a significant research effort has been directed towards models of random walks that do not satisfy these assumptions. One of the most important of these models is that of random walk in random environment (RWRE). In the talk I will describe RWRE, compare its behavior to that of classical random walk and present a few predictable as well as a few surprising results. I will conclude with some open problems.