The human motor system controls a large number of independent degrees of freedom simultaneously, and is capable of learning a seemingly infinite amount of movement skills, vastly surpassing such abilities of any man-made robot. The computational and neuronal mechanisms of human dexterity and adaptation abilities remain elusive. It has been recently suggested that one of the computational brain mechanisms allowing such a rich movement repertoire might be “structure learning” (Braun et al., 2009b). After extensive practice with motor tasks sharing structural similarities (e.g. different dancing movements, or different sword techniques), new tasks of the same type can be learnt faster. According to the structure learning hypothesis, such rapid generalisation of related motor skills relies on learning the dynamic and kinematic relationships shared by this set of skills. As a consequence, motor adaptation becomes constrained, effectively leading to a dimensionality reduction of the learning problem; at the same time, adaptation to tasks lying outside the structure becomes biased towards the structure. We tested these predictions by investigating how previously learnt structures influence subsequent motor adaptation and found that after extensive training with both kinematic or dynamic perturbations, adaptation to unpractised, diagonal, perturbations happened along the previously learnt structure (vertical or horizontal), and resulting adaptation trajectories were curved. We further present several computational models that can account for this behaviour: correlated distribution of motor primitives, changed Bayesian prior or Bayesian network with a hidden variable. These models make different predictions with respect to structure extrapolation; in a series of experiments we did not observe any evidence for structure extrapolation and conclude that the observed effects are probably explained by the changed Bayesian priors. Finally, we present a series of experiments on path tracking, where subjects develop a skill of path tracking in the absence of any external perturbations. Relationship with structure learning is discussed.