Myoelectric-computer interfaces (MCIs) provide a unique opportunity to study mechanisms of motor learning and adaptation as they allow the creation of abstract sensorimotor tasks disassociated from biomechanical constraints, and the manipulation of visuomotor mappings at the level of individual muscles. In addition, study of MCI use provides a useful basis for designing optimal prosthetics, by understanding how the motor system deals with new patterns of muscle co-ordination. Here I used MCI tasks in order to examine subjects’ ability to learn and adapt to abstract sensorimotor mappings. In the tasks, subjects moved a 2D cursor controlled by electromyogram (EMG) recorded from between two and eight hand and forearm muscles. Each muscle was assigned a direction of action (DoA) and cursor position was determined using the vector sum of the EMG. Subjects were able to quickly learn abstract mappings, and adapt successfully to rotations of the full muscle-DoA mapping (global) and rotations where subsets of the muscle-DoA relationships were perturbed (local). Adaptation was biased by naturalistic behaviour, but that did not impede subjects from solving the tasks. Strategies that subjects used to solve local adaptation tasks could be biased via tDCS of M1 and the cerebellum. Global and local rotations were adapted to in different ways, with local adaptation lacking the after-effects associated with classical adaptation, indicating the creation of a new internal model for the adapted state, as opposed to alteration of a single one. tDCS affected these forms of adaptation in different ways, with stimulation of M1 predominantly affecting global adaptation and stimulation of the cerebellum predominantly affecting local adaptation. In conclusion, I have demonstrated that the motor system can successfully learn and adapt to abstract motor tasks, with the underlying processes being dependent on M1 and the cerebellum in ways that have a structural dependence.