Exuberant social and linguistic development characterize the first years of life for the typical child, whereas deviant, stymied, or regressive development mark these years for the child with autism. The brain bases underlying the emergence of complex cognitive capacities in typical and atypical development remain speculative due to the current difficulty in acquiring functional brain imaging data from infants and toddlers without motion artifact. Through the use of a novel technique in which functional magnetic resonance imaging (fMRI) data are collected during natural sleep, this dissertation provides the first fMRI studies of functional brain organization in 1-4 year old typically-developing children and 2-3 year- old children with autism. The feasibility of the sleep fMRI technique was investigated through two studies of typically-developing children. First, presentation of auditory and visual stimuli to typical 2-4 year-old children during sleep revealed differential activity between and within stimulus modalities. Furthermore, stimulus-independent auditory and visual networks were identified. Second, presentation of speech and nonspeech stimuli to two groups of typical children (toddlers and 3 year-olds) revealed age-related differences in the brain response to speech. Specifically, toddlers recruited an extended network pattern of brain activity encompassing frontal, occipital, and cerebellar regions. The 3 year- olds, however, showed a more focal pattern of BOLD activity primarily within bilateral superior temporal regions. This time-delimited, extended pattern of brain activity in the typical toddlers may allow for the rapid burst in language growth seen during the second year of life. These studies add to the growing body of literature indicating that stimulus discrimination and intrinsic functional networks persist during sleep. When speech and nonspeech stimuli were presented to 2-3 year old children with autism spectrum disorder (ASD), a pattern of brain activity was identified that differed from two typically- developing control groups. In comparison to their mental age-matched controls (MA), the ASD group recruited a reduced number of brain regions within the 'extended network'. In comparison to their chronological age-matched controls (CA), the ASD group showed a greater reliance on right hemisphere brain regions. The discussion suggests possible implications of an early, right hemisphere, deviant developmental trajectory for the etiology of autism