Motor-transformation learning theory asserts that people learn through experience what stimulus transformations are under the control of their behavior. More specifically, it asserts that the parameter values of certain predetermined transformation groups are learned. This theory was inferred, in the first place, from research on adaptation to optical rearrangement—in particular, from position-constancy adaptation in inverting-spectacles experiments, prism-displacement experiments, and in more recent computer-controlled feedback experiments. The detailed characteristics of position-constancy adaptation are found to be consistent with the theory. Diverse consequences radiate from the theory for other human abilities, both in perception and in memory retrieval. These diverse implications are tested in studies of (a) learning to manipulate ‘objects’ in an artificial computer-controlled visual space; (b) learning to compute, in the absence of overt action, the consequences of such action; (c) learning how to access the features of prior stimuli by the execution of motor actions.