The neurophysiological basis for binocular control of eye movements in primates has been characterized by a scientific controversy that has its origin in the historical conflict of Hering and Helmholtz in the 19th century. This review focuses on two hypotheses, linked to that conflict, that seek to account for binocular coordination – Hering’s Law vs. uniocular control of each eye. In an effort to manage the length of the review, the focus is on extracellular single-unit studies of premotor eye movement cells and extraocular motoneurons. In the latter half of the 20th century, these studies provided a wealth of neurophysiological data pertaining to the control of vergence and conjugate eye movements. The data were initially supportive of Hering’s Law. More recent data, however, have provided support for uniocular control of each eye consistent with Helmholtz’s original idea. The controversy is far from resolved. New anatomical descriptions of the disparate inputs to multiply and singly innervated extraocular muscle fibers challenge the concept of a ‘final common pathway’ as they suggest there may be separate groups of motoneurons involved in vergence and conjugate control of eye position. These data provide a new challenge for interpretation of uniocular premotor control networks and how they cooperate to produce coordinated eye movements.