The oculomotor system is a useful model for the study of purposeful movements. Rotations of the eyes are produced by three pairs of extraocular muscles that are innervated by motor neurons from the III, IV and VI cranial nerve nuclei. A saccadic eye movement is produced when the appropriate motor neurons produce a burst of spikes, followed by tonic firing at the correct rate to maintain the eye's new position. The commands for horizontal components of saccades originate in the pons and medulla. Omnipause neurons fire tonically during fixation, but stop firing during saccades; long-lead burst neurons and excitatory burst neurons fire before and during saccades. Excitatory burst neurons synapse onto motor neurons and drive the motor neuron pulse of activity. Neurons in the prepositus and vestibular nuclei fire tonically and drive the step of activity that maintains eye position. Microstimulation of neurons in the pontine reticular formation produces horizontal eye movements. Neurons in the rostral midbrain that have similar properties drive vertical eye movements. The duration and velocity of saccades are determined by the duration and maximal firing rate of the bursts of activity produced by these neurons. The horizontal and vertical components of oblique saccades are coordinated. The shorter of the two components proceeds at a lower velocity than normal so that the two will have the same duration and the movement will not be curved. The onsets of the two components are coordinated by omnipause neurons in the pons. The torsional component of saccadic eye movements is stereotyped and obeys Donders' law: for any direction of the line of sight, if the head is upright and stationary, the eye will assume a given degree of torsion, regardless of the route taken by the eye to reach its position. Saccades also obey Listing's law, which specifies the orientation of the globe for each gaze position. It is unclear how these laws are implemented, but identifying the mechanisms is an important part of understanding the generation of saccades. Neurons in the superior colliculus (SC) provide the main input to the pontine and midbrain pulse–step generators. Microstimulation of these neurons produces saccades in head-restrained animals, and coordinated head and eye movements in head-unrestrained animals. The size and direction of the movements produced are primarily determined by the position of the stimulation in the SC. Models of saccade generation assume that saccades are under feedback control and that the feedback comes from corollary discharge. Models differ in the implementation of this feedback, but it has not been possible to determine the type of feedback signal used or the site of the comparator. Reasons for this include the fact that signals that are separate in models might be intermingled in the brain, preventing selective lesioning of these signals, and that different models produce similar signals. Models also tend to use population signals, but in terms of electrophysiology, it is hard to know what the population signal is at any given time. The problems faced by oculomotor researchers are mirrored in other areas of systems neuroscience.