Autism spectrum disorders are a group of lifelong disabilities that affect people's ability to communicate and to understand social cues. Research into applying robots as therapy tools has shown that robots seem to improve engagement and elicit novel social behaviors from people (particularly children and teenagers) with autism. Robot therapy for autism has been explored as one of the first application domains in the field of socially assistive robotics (SAR), which aims to develop robots that assist people with special needs through social interactions. In this review, we discuss the past decade's work in SAR systems designed for autism therapy by analyzing robot design decisions, human-robot interactions, and system evaluations. We conclude by discussing challenges and future trends for this young but rapidly developing research area.