The purpose of this paper is to review the kinematics and dynamics of the vestibulo-ocular reflex (VOR) in three dimensions. We give a brief, didactic tutorial on vectors and matrices and their importance as representational schemes for describing the kinematics and dynamics of the angular and linear accelerations that activate the vestibular system. We show how the vectors associated with angular and linear head accelerations are transformed by the peripheral and central vestibular systems to drive the oculomotor system to produce eye movements in three-dimensional space. We also review critical questions and controversies related to the compensatory and orientation behavior of the VOR. One such question is how the central vestibular system distinguishes tilts of the head, which generate interaural linear acceleration from translations along the interaural axis. Another question is how the velocity-position integrator is implemented centrally. The review has been placed in the context of a model that explains the behavior of the VOR in three dimensions. Model processes have been related to peripheral and central neural behavior in order to gain insight into the nature of the three-dimensional organization and the controversial questions that are addressed.