Neuronal oscillations are ubiquitous in the brain and may contribute to cognition in several ways: for example, by segregating information and organizing spike timing. Recent data show that delta, theta and gamma oscillations are specifically engaged by the multi-timescale, quasi-rhythmic properties of speech and can track its dynamics. We argue that they are foundational in speech and language processing, 'packaging' incoming information into units of the appropriate temporal granularity. Such stimulus-brain alignment arguably results from auditory and motor tuning throughout the evolution of speech and language and constitutes a natural model system allowing auditory research to make a unique contribution to the issue of how neural oscillatory activity affects human cognition.