The classical view of the speech and language neural system is that of a hierarchy of interdependent modules, enabling the progressive transformation of a continuous acoustic stream into an articulated series of concepts. This modular and hierarchical view follows from the combination of lesion studies (double dissociations) and hypothesis-based factorial designs in which only a few sensory or cognitive factors are varied at a time. In the last ten years, however, data-driven explorations of large neuroimaging datasets have allowed for a more agnostic approach, and led to a whole new view where segregated hierarchically organized modules seem to give way to continuous multidimensional representations, with e.g. a distributed semantic system. While both approaches have brought about significant contributions to speech and language neuroscience, making coherent sense of them represents a substantial challenge. In this review article, we synthesize methodological and experimental findings from the speech and language neuroscience literature, dissecting strength and pitfalls of each approach and suggesting ways in which approaches could be integrated.