Language lies at the heart of our experience as humans and disorders of language acquisition carry severe developmental costs. Rhythmic processing lies at the heart of language acquisition. Here, I review our understanding of the perceptual and neural mechanisms that support language acquisition, from a novel amplitude modulation perspective. Amplitude modulation patterns in infant- and child-directed speech support the perceptual experience of rhythm, and the brain encodes these rhythm patterns in part via neuroelectric oscillations. When brain rhythms align themselves with (entrain to) acoustic rhythms, speech intelligibility improves. Recent advances in the auditory neuroscience of speech processing enable studies of neuronal oscillatory entrainment in children and infants. The "amplitude modulation phase hierarchy" theoretical perspective on language acquisition is applicable across languages, and cross-language investigations adopting this novel perspective would be valuable for the field.