How does the brain compute? To address this question, mathematical modelers, neurophysiologists, and psychophysicists have sought behaviors that provide evidence of specific neural computations. Human motor behavior consists of several such computations [Shadmehr, R., Wise, S.P. (2005). MIT Press: Cambridge, MA], such as the transformation of a sensory input to a motor output. The motor system is also capable of learning new transformations to produce novel outputs; humans have the remarkable ability to alter their motor output to adapt to changes in their own bodies and the environment [Wolpert, D.M., Ghahramani, Z. (2000). Nat. Neurosci., 3: 1212-1217]. These changes can be long term, through growth and changing body proportions, or short term, through changes in the external environment. Here we focus on trial-by-trial adaptation, the transformation of individually sensed movements into incremental updates of adaptive control. These investigations have the promise of revealing important basic principles of motor control and ultimately guiding a new understanding of the neuronal correlates of motor behaviors.