How do young children learn to organize the statistics of communicative input across milliseconds and months? Developmental science has made progress in understanding how infants learn patterns in language and how infant-directed speech is engineered to ease short-timescale processing, but less is known about how they link perceptual experiences across multiple levels of processing within an interaction (from syllables to stories) and across development. In this article, we propose that three domains of research - statistical summary, neural processing hierarchies, and neural coupling - will be fruitful in uncovering the dynamic exchange of information between children and adults, both in the moment and in aggregate. In particular, we discuss how the study of brain-to-brain and brain-to-behavior coupling between children and adults will further our understanding of how children's neural representations become aligned with the increasingly complex statistics of communication across timescales.