Children with language-learning impairments (LLI) form a heterogeneous population with the majority having both spoken and written language deficits as well as sensorimotor deficits, specifically those related to dynamic processing. Research has focused on whether or not sensorimotor deficits, specifically auditory spectrotemporal processing deficits, cause phonological deficit, leading to language and reading impairments. New trends aimed at resolving this question include prospective longitudinal studies of genetically at-risk infants, electrophysiological and neuroimaging studies, and studies aimed at evaluating the effects of auditory training (including musical training) on brain organization for language. Better understanding of the origins of developmental LLI will advance our understanding of the neurobiological mechanisms underlying individual differences in language development and lead to more effective educational and intervention strategies. This review is part of the INMED/TINS special issue "Nature and nurture in brain development and neurological disorders", based on presentations at the annual INMED/TINS symposium (http://inmednet.com/).