Neural prosthetic systems aim to help disabled patients suffering from a range of neurological injuries and disease by using neural activity from the brain to directly control assistive devices. This approach in effect bypasses the dysfunctional neural circuitry, such as an injured spinal cord. To do so, neural prostheses depend critically on a scientific understanding of the neural activity that drives them. We review here several recent studies aimed at understanding the neural processes in premotor cortex that precede arm movements and lead to the initiation of movement. These studies were motivated by hypotheses and predictions conceived of within a dynamical systems perspective. This perspective concentrates on describing the neural state using as few degrees of freedom as possible and on inferring the rules that govern the motion of that neural state. Although quite general, this perspective has led to a number of specific predictions that have been addressed experimentally. It is hoped that the resulting picture of the dynamical role of preparatory and movement-related neural activity will be particularly helpful to the development of neural prostheses, which can themselves be viewed as dynamical systems under the control of the larger dynamical system to which they are attached.