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In many domains of human cognition, hierarchically structured representations are thought to play a key role. In this paper, we start with some foundational definitions of key phenomena like “sequence” and “hierarchy," and then outline potential signatures of hierarchical structure that can be observed in behavioral and neuroimaging data. Appropriate behavioral methods include classic ones from psycholinguistics along with some from the more recent artificial grammar learning and sentence processing literature. We then turn to neuroimaging evidence for hierarchical structure with a focus on the functional MRI literature. We conclude that, although a broad consensus exists about a role for a neural circuit incorporating the inferior frontal gyrus, the superior temporal sulcus, and the arcuate fasciculus, considerable uncertainty remains about the precise computational function(s) of this circuitry. An explicit theoretical framework, combined with an empirical approach focusing on distinguishing between plausible alternative hypotheses, will be necessary for further progress.