The study of the motor cortex in behaving monkeys during the past 20 years has provided important information on the brain mechanisms underlying motor control. With respect to reaching movements in space, several aspects of motor cortical function concerning the specification of the direction of movement have now been elucidated and are reviewed in this article. The activity of single cells in the motor cortex is broadly tuned with respect to the direction of reaching, so that the discharge rate is highest with movements in a preferred direction and decreases progressively with movements made in directions more and more away from the preferred one. Thus the neural command for the direction of reaching can be regarded as an ensemble of cell vectors, with each vector pointing in the cell's preferred direction and having a length proportional to the change in cell activity. The outcome of this population code can be visualized as a vector that points in the direction of the upcoming movement during the reaction time, during an instructed delay period, and during a memorized delay period. Moreover, when a mental transformation is required for the generation of a reaching movement in a different direction from a reference direction, the population vector provides a direct insight into the nature of the cognitive process by which the required transformation is achieved.