Irreversible phenomena are of fundamental importance because they characterize a direction of time. Irreversibility has been observed in three different physical situations, namely, in thermodynamics (monotonic increase of entropy), quantum theory (measurement process), and cosmology (black holes and their entropy). There is no consensus on how these three kinds of irreversibility are connected, and whether there is any common ground that can explain them consistently, or if one of them is more fundamental than the others. A solution to the above questions is to work with a physical theory that picks a preferred direction of time. Collapse models, as quantum non-linear and stochastic theories, may provide us with such a solution. After discussing the features of collapse models in detail, we review the phenomenological implications of these models, with particular attention to the aforementioned issues.
