Robots manipulate with super-human speed and dexterity on factory floors. But yet they fail even under moderate amounts of clutter or uncertainty. However, human teleoperators perform remarkable acts of manipulation with the same hardware. My research goal is to bridge the gap between what robotic manipulators can do now and what they are capable of doing. What human operators intuitively possess that robots lack are models of interaction between the manipulator and the world that go beyond pick-and-place. I will describe our work on nonprehensile physics-based manipulation that has produced simple but effective models, integrated with proprioception and perception, that has enabled robots to fearlessly push, pull, and slide objects, and reconfigure clutter that comes in the way of their primary task. But human environments are also filled with humans. Collaborative manipulation is a dance, demanding the sharing of intentions, inferences, and forces between the robot and the human. I will also describe our work on the mathematics of human-robot interaction that has produced a framework for collaboration using Bayesian inference to model the human collaborator, and trajectory optimization to generate fluent collaborative plans. Finally, I will talk about our new initiative on assistive care that focuses on marrying physics, human-robot collaboration, control theory, and rehabilitation engineering to build and deploy caregiving systems.