This thesis discusses the use of adaptive control within human-robot interaction, and in particular rehabilitation robots, in order to change the perceived closed-loop system dynamics and compensate for unexpected and changing subject behaviors. I first motivate the use of controllers during robotic rehabilitation through a human-subjects study, in which I juxtapose interaction controllers and a novel motor learning protocol, and find that haptic guidance and error augmentation can improve the retention of trained behavior after feedback is removed. Next, I develop an adaptive controller for rigid upper-limb rehabilitation robots, which uses sensorless force estimation to minimize the amount of robotic assistance while also bounding the subject's trajectory errors. Finally, I discuss the use of time domain adaptive control in the context of physically compliant rehabilitation robots---in particular, series elastic actuators---where I discover that adaptive techniques enable passively rendering virtual environments not achievable using existing practices. Each of these adaptive controllers is developed using the theoretical framework of Lyapunov stability analysis, and is tested on single degree-of-freedom robotic hardware. I conclude that adaptive control provides an avenue for safe robotic interaction, both through stability analysis and physical compliance, and can adjust to subjects of various impairment levels to ensure that training is meaningful, in the sense that desired trajectories, interactions, and long-term effects are achieved.