Purpose Investigations into the nature of communication disorders in autistic individuals increasingly evaluate neural responses to speech stimuli. This integrative review aimed to consolidate the available data related to speech and language processing across levels of stimulus complexity (from single speech sounds to sentences) and to relate it to the current theories of autism. Method An electronic database search identified peer-reviewed articles using event-related potentials or magnetoencephalography to investigate auditory processing from single speech sounds to sentences in autistic children and adults varying in language and cognitive abilities. Results Atypical neural responses in autistic persons became more prominent with increasing stimulus and task complexity. Compared with their typically developing peers, autistic individuals demonstrated mostly intact sensory responses to single speech sounds, diminished spontaneous attentional orienting to spoken stimuli, specific difficulties with categorical speech sound discrimination, and reduced processing of semantic content. Atypical neural responses were more often observed in younger autistic participants and in those with concomitant language disorders. Conclusions The observed differences in neural responses to speech stimuli suggest that communication difficulties in autistic individuals are more consistent with the reduced social interest than the auditory dysfunction explanation. Current limitations and future directions for research are also discussed.