The organization of language-relevant brain systems was examined in normally developing and language-impaired children. Atypical patterns of brain activity were observed in subsets of children with specific language impairment (SLI) for both sensory (auditory and visual) and language processing. However, it was not the same groups of children who displayed abnormalities across the different tasks. The results supported a multiple-factors and multiple-subtypes framework for interpreting the neurobiology of SLI. The roots of SLI were also considered in normal infants and late talkers in studies of primary language acquisition. These studies suggest that the organization of neural systems important in language acquisition display dramatic changes during this time. Some of these are linked to the attainment of language milestones and appear to be independent of chronological age. Moreover, abnormalities in the lateral organization of electrophysiological activity may help predict which late talkers will catch up and who will later display SLI. More generally, the event-related potential technique is a powerful tool in studying the neurobiology of language and language impairment.