Conventional neurorehabilitation appears to have little impact on impairment over and above that of spontaneous biological recovery. Robotic neurorehabilitation has the potential for a greater impact on impairment due to easy deployment, its applicability across of a wide range of motor impairment, its high measurement reliability, and the capacity to deliver high dosage and high intensity training protocols. We first describe current knowledge of the natural history of arm recovery after stroke and of outcome prediction in individual patients. Rehabilitation strategies and outcome measures for impairment versus function are compared. The topics of dosage, intensity, and time of rehabilitation are then discussed. Robots are particularly suitable for both rigorous testing and application of motor learning principles to neurorehabilitation. Computational motor control and learning principles derived from studies in healthy subjects are introduced in the context of robotic neurorehabilitation. Particular attention is paid to the idea of context, task generalization and training schedule. The assumptions that underlie the choice of both movement trajectory programmed into the robot and the degree of active participation required by subjects are examined. We consider rehabilitation as a general learning problem, and examine it from the perspective of theoretical learning frameworks such as supervised and unsupervised learning. We discuss the limitations of current robotic neurorehabilitation paradigms and suggest new research directions from the perspective of computational motor learning.