Computational motor control covers all applications of quantitative tools for the study of the biological movement control system. This paper provides a review of this field in the form of a list of open questions. After an introduction in which we define computational motor control, we describe: a Turing-like test for motor intelligence; internal models, inverse model, forward model, feedback error learning and distal teacher; time representation, and adaptation to delay; intermittence control strategies; equilibrium hypotheses and threshold control; the spatiotemporal hierarchy of wide sense adaptation, i.e., feedback, learning, adaptation, and evolution; optimization based models for trajectory formation and optimal feedback control; motor memory, the past and the future; and conclude with the virtue of redundancy. Each section in this paper starts with a review of the relevant literature and a few more specific studies addressing the open question, and ends with speculations about the possible answer and its implications to motor neuroscience. This review is aimed at concisely covering the topic from the author's perspective with emphasis on learning mechanisms and the various structures and limitations of internal models.