We review the potential that brain oscillations have for improving our understanding of the processing, evolution and development of natural language. The different ‘grammars’ of brain rhythms can account for different perceptual and cognitive functions, and we argue that this includes language. We aim to address six distinct questions – the What, How, Where, Who, Why, and When questions – pertaining to oscillatory investigations of language. We review how language deficits found in clinical conditions like autism, schizophrenia and dyslexia can be satisfactorily construed in terms of an abnormal, disorder-specific pattern of brain rhythmicity. Lastly, we argue that an eco-evo-devo approach to language is compulsory.