Recent studies have shown that children with autism may be interested in playing with an interactive robot. Moreover, the robot can engage these children in ways that demonstrate essential aspects of human interaction, guiding them in therapeutic sessions to practice more complex forms of interaction found in social human-to-human interactions. We review published articles on robot-assisted autism therapy (RAAT) to understand the trends in research on this type of therapy for children with autism and to provide practitioners and researchers with insights and possible future directions in the field. Specifically, we analyze 38 articles, all of which are refereed journal articles, that were indexed on Web of Science from 2009 onward, and discuss the distribution of the articles by publication year, article type, database and journal, research field, robot type, participant age range, and target behaviors. Overall, the results show considerable growth in the number of journal publications on RAAT, reflecting increased interest in the use of robot technology in autism therapy as a salient and legitimate research area. Factors, such as new advances in artificial intelligence techniques and machine learning, have spurred this growth.