As human beings, we can understand spoken language, recognize the opening bars of Beethoven's 5th Symphony, notice the tide-induced fluctuations of the level of the ocean, predict the color of traffic lights, and identify many more of the ubiquitous temporal regularities that characterize our daily environment. How does the human brain detect, identify, process and leverage those regularities in spite of their striking diversity? In this dissertation, I studied the mechanisms through which the human brain acquires knowledge of sequences and of regularities they may entail. To do so, I recorded behavioural and neural responses to auditory binary sequences characterized by various types of regularities. In parallel, I derived mathematical models of sequence processing that rest upon normative principles of probabilistic inference, but that are yet characterized by different computational architectures, and used human data to arbitrate among them. Using this same general approach, I investigated three different facets of the human sensitivity to sequences. Firstly, I demonstrated that a simple machinery for inferring transition structures between sequence items supports various aspects of the human perception of sequences encountered in seemingly disparate studies. Secondly, I then found that this learning algorithm was implemented in distinct brain systems which extracted statistical trends over different timescales, thereby providing a mechanistic explanation for the human sensitivity to both global statistical biases and to the recent history of observations. In addition to statistical learning, humans also possess the ability to quickly detect and identify deterministic rules. Thirdly, I showed that statistics and rules correspond to two distinct hypothesis spaces, instead of a continuum; and that human subjects could rationally arbitrate among them given the observed sequence. Altogether, my investigations of the cognitive foundations, computational principles and neural architectures supporting sequence processing suggest that the human brain is equipped with several systems that conform to normative principles of probabilistic inference but that are specialized in different aspects of sequences, thereby providing a putative explanation for the human perception of a vast repertoire of temporal regularities.