The general theme of the talk pertains to the question of understanding how paths of random walks can create large separating interfaces. This question has in particular been investigated in the context of random walk on a discrete cylinder with a large connected base, and when discussing the presence or absence of a giant component in the complement of the trajectory of a random walk on a large discrete torus. We will present an overview of some of the results, and paradigms, which have now emerged and explain how the above problems are related to questions of ercolation and to the model of random interlacements.