The neural velocity to position integrators transform the saccade related signal of the burst generators into an eye position related tonic signal they convey to motoneurons. They are largely confined to three heavily interconnected midbrain structures: 1) The interstitial nucleus of Cajal (NIC), 2) The nucleus prepositus hypoglossi (NPH), 3) The vestibular nuclei (VN). Integration in the horizontal and vertical planes is accomplished largely independently by the NPH-VN and the NIC-VN complexes, respectively. Cells in these regions carry a more or less intense phasic signal related to saccades and a tonic signal related to eye position. Depending on the relationship between the rate of their discharge and the position of the eyes, these cells have been further subdivided into regular or irregular, more or less sensitive, and bi-directionally or uni-directionally modulated. The present review provides a brief description of their discharge pattern and that of burst neurons and extraocular motoneurons. Then, evidence concerning the input-output connections of relevant cell classes is summarized. Finally, several modelling attempts to simulate the neural velocity-to-position integrators are presented and their verisimilitude is evaluated in the light of psychophysical, anatomical, physiological and neurological evidence.