Reaching movements have the well-defined goal of bringing the hand to the location of an object of interest. For neuroscientists a basic problem to be solved is how the nervous system transforms the visual information concerning the location of the object in space into a pattern of muscle activity necessary to bring the hand to it. According to Descartes, spirits passing from the eyes impinge on the pineal gland, causing it to lean in one direction or another; this leaning of the gland pulls on filaments (nerves) attached to the muscles. Modern treatments, instead, tend to decompose this process into sequences of transformations between informational representations. Such transformations lead from a description of the target in visual coordinates to an expression of the movement in muscle space by way of various internal representations. The organization of such internal representations has implications for the types of transformations actually performed in the brain. Recent psychophysical, neurophysiological, and computational approaches to study the cortical representations of reaching movements are yielding complementary data on this issue.