How are hierarchically structured sequences of objects, events or actions learned from experience and represented in the brain? When several streams of regularities present themselves, which will be learned and which ignored? Can statistical regularities take effect on their own, or are additional factors such as behavioral outcomes expected to influence statistical learning? Answers to these questions are starting to emerge through a convergence of findings from naturalistic observations, behavioral experiments, neurobiological studies, and computational analyses and simulations. We propose that a small set of principles are at work in every situation that involves learning of structure from patterns of experience and outline a general framework that accounts for such learning.