Linguistic prosody involves the rhythm and melody of speech. It implicitly enhances or modifies the explicit meaning of spoken words. The literature on linguistic prosody related to autism spectrum disorder deals both with the production and perception of a broad range of linguistic functions. These functions range from the formal encoding of grammatical features (e.g. lexical stress, syntactic structure) to the less formal, more intuitive signalling of pragmatic or interactional aspects (speech acts, information structure, turn‐taking in conversation). This narrative review reports mixed results from 51 studies, with tentative evidence for greater differences in the perception of intuitive functions. Apart from considerable methodological differences across the different studies, much of the variability in the results is due to the wide range of ages investigated, since difficulties encountered by autistic children do not always persist into adulthood and compensatory strategies can be learnt for using prosody in communication.