As robotic technologies become more accessible and affordable, their potential to improve health and social outcomes for individuals with neurodevelopmental disabilities, including autism is increasingly recognised. Current research into the use of social and humanoid robots is promising, reporting improvements in a range of outcomes including social communication, engagement, learning and behaviour. However, these outcomes are influenced by the characteristics of the individual, the robot design, sensors employed, the nature of the human-robot interaction, and the technologies embedded in the system. There is a need to critically explore the use of Socially Assistive Robots (SARs) for autistic people, in terms of the desired outcomes, enablers and barriers to their use, discussing potential challenges, gaps in current evidence and future directions. If designed and developed well, taking a multidisciplinary approach, there is immense potential in the use of SARs to improve the lives of people with neurodevelopmental disabilities.