Entrainment is the tendency of people to behave similarly during an interaction. It occurs on different levels of behaviour, including speech, and has been associated with pro-social behaviour and increased rapport. This review paper outlines the current understanding of linguistic entrainment, particularly at the speech level, in individuals with autism spectrum disorder (ASD), a disorder that is associated with social difficulties and unusual prosody. Aberrant entrainment patterns in individuals with ASD could thus contribute to both their perceived unusual prosody and their social difficulties. Studying the relationship between speech entrainment and ASD holds great potential for applied benefits in utilizing this knowledge for pre-screening or diagnosis, monitoring progress longitudinally, and intervention practices. Our findings suggest that research on entrainment in ASD is sparse and exploratory, and the ecological validity of experimental paradigms varies. Moreover, there is little consistency in methodology and results vary between studies, which highlights the need for standardized methods in entrainment research. A promising way to standardize methods, facilitate their use, and extend them to everyday clinical practice, is by implementing automatic methods for speech analysis and adhering to open-science principles.