A central goal of the Neurosciences is to provide an account of how the brain works in terms of cell groups organised into pattern generating networks. This review focuses on the neural network that generates the rapid movements of the eyes that are called saccades. A brief description of the metrical and dynamical properties of saccades is provided first. Data obtained from lesion and electrical stimulation experiments are then described; these indicate that the relevant neural machinery spreads over at least 10 distinct cortical and subcortical regions of the brain. Each one of these regions harbors several distinct classes of saccade related cells (i.e. cells whose discharge encodes the metrical and often dynamical properties of saccades). The morphological and physiological properties of about 30 saccade related cell classes are described. To generate the signals they carry, and therefore saccades, distinct classes of cells influence each other in a non-random manner. Anatomical evidence is provided that indicates the existence of about 100 distinct connections established between saccade related neurons. The overall picture of the saccadic system that emerges from these studies is one of intricate complexity. In part this is due to the presence of at least 3, multiply interconnected negative feedback loops. Several computational models of the saccadic system have been proposed in an attempt to understand the functional significance of the simultaneous operation of these loops. An evaluation of these models demonstrates that besides providing a coherent summary of the data that concern it, successful models of the saccadic system generate realistic saccades (in precise quantitative psychophysical terms) when their elements are stimulated, produce abnormal saccades, reminiscent of those encountered in the clinic, when their elements are disabled, while their constituent units display realistic discharge patterns and are connected in a manner that respects anatomy.