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More than 1 billion people in the world are estimated to experience significant disability. These disabilities can impact people's ability to independently conduct activities of daily living, including ambulating, eating, dressing, taking care of personal hygiene, and more. Mobile and manipulator robots, which can move about human environments and physically interact with objects and people, have the potential to assist people with disabilities in activities of daily living. Although the vision of physically assistive robots has motivated research across subfields of robotics for decades, such robots have only recently become feasible in terms of capabilities, safety, and price. More and more research involves end-to-end robotic systems that interact with people with disabilities in real-world settings. In this article, we survey papers about physically assistive robots intended for people with disabilities from top conferences and journals in robotics, human–computer interactions, and accessible technology, to identify the general trends and research methodologies. We then dive into three specific research themes—interaction interfaces, levels of autonomy, and adaptation—and present frameworks for how these themes manifest across physically assistive robot research. We conclude with directions for future research.