Designing safe and reliable robotic assistance for caregiving is a grand challenge in robotics. A sixth of the United States population is over the age of 65 and in 2014 more than a quarter of the population had a disability. Robotic caregivers could positively benefit society; yet, physical robotic assistance presents several challenges and open research questions relating to teleoperation, active sensing, and autonomous control. In this talk, I will present recent techniques and technology that my group has developed towards addressing core challenges in robotic caregiving. First, I will introduce two wearable sensorized interfaces that enable people with severe loss of motor and hand function (due to spinal cord injury or neurodegenerative diseases) to embody physically assistive mobile manipulators. I will then present our recent work in robot learning, including policy learning and dynamics modeling, to perform complex manipulation of deformable garments and blankets around the human body.