Assistive machines - like power wheelchairs, robotic arms, exoskeletons, prostheses - are vital for enabling independence for people with severe motor impairments. However, there exists a paradox, where often the more severe a person's impairment, the less able they are to operate these very machines which might improve their quality of life. Here robotics technologies have the potential to transform the field of human health and rehabilitation: by turning the machine into a robot, that can operate itself autonomously and share the control burden. It will be crucial that these robots adapt to the human user's unique preferences and abilities, and how both change over time is crucial for achieving widespread adoption and acceptance, and especially if attached to a human's body to provide physical assistance. <br/><br/>There has been limited study of robot learning from non-experts, and the domain of motor-impaired teachers is even more challenging: their control signals are noisy (due to artifacts in the motor signal) and sparse (if providing motor commands is more effort), and filtered through an interface. Rather than treat these constraints as limitations, the proposed work hypothesizes that such constraints become advantageous for machine learning algorithms that exploit unique characteristics (like problem-space sparsity) of control and feedback signals from motor-impaired humans. The work develops multiple novel machine learning algorithmic techniques, (1) that reason explicitly about the control interface and how it interacts with the full robot control space; (2) that derive information about the human's control patterns and task requirements, from variability in the human's teleoperation commands; and (3) which include the design of adaptation cues informed by reward- and example-based feedback from motor-impaired teachers. The proposed work also performs subject studies with motor-impaired end-users operating multiple robotic platforms, both to explore this problem space and assess the functionality and user acceptance of the contributed algorithmic techniques.