Autonomous robots have the potential to serve as versatile caregivers that improve quality of life for millions of people with disabilities worldwide. Yet, physical robotic assistance presents several challenges, including risks associated with physical human-robot interaction, difficulty sensing the human body, and a lack of tools for benchmarking and training physically assistive robots. In this talk, I will present techniques towards addressing each of these core challenges in robotic caregiving. First, I will introduce a method inspired by human perspective-taking which allow assistive robots to predict how their future actions will apply forces to a person’s body. I will then describe capacitive servoing, a new sensing technique for robots to sense the human body and track trajectories along the body. Finally, I will show how we can develop intelligent robotic caregivers via simulation and virtual reality, and I will introduce Assistive Gym, the first physics simulation framework for benchmarking and training physically assistive robots.