Do people use sensori-motor cortices to understand language? Here we review neurocognitive studies of language comprehension in healthy adults and evaluate their possible contributions to theories of language in the brain. We start by sketching the minimal predictions that an embodied theory of language understanding makes for empirical research, and then survey studies that have been offered as evidence for embodied semantic representations. We explore four debated issues: first, does activation of sensori-motor cortices during action language understanding imply that action semantics relies on mirror neurons? Second, what is the evidence that activity in sensori-motor cortices plays a functional role in understanding language? Third, to what extent do responses in perceptual and motor areas depend on the linguistic and extra-linguistic context? And finally, can embodied theories accommodate language about abstract concepts? Based on the available evidence, we conclude that sensori-motor cortices are activated during a variety of language comprehension tasks, for both concrete and abstract language. Yet, this activity depends on the context in which perception and action words are encountered. Although modality-specific cortical activity is not a sine qua non of language processing even for language about perception and action, sensori-motor regions of the brain appear to make functional contributions to the construction of meaning, and should therefore be incorporated into models of the neurocognitive architecture of language.