In the last decade, the involvement of neural oscillatory mechanisms in speech comprehension has been increasingly investigated. Current evidence suggests that low-frequency and high-frequency neural entrainment to the acoustic dynamics of speech are linked to its analysis. One crucial question is whether acoustical processing primarily modulates neural entrainment, or whether entrainment instead reflects linguistic processing. Here, we review studies investigating the effect of linguistic manipulations on neural oscillatory activity. In light of the current findings, we argue that theta (3-8 Hz) entrainment may primarily reflect the analysis of the acoustic features of speech. In contrast, recent evidence suggests that delta (1-3 Hz) and high-frequency activity (>40 Hz) are reliable indicators of perceived linguistic representations. The interdependence between low-frequency and high-frequency neural oscillations, as well as their causal role on speech comprehension, is further discussed with regard to neurophysiological models of speech processing.