A central problem in motor control is to understand how different mobile segments are coordinated to achieve a common goal. In natural conditions, where the head is not restrained, a combination of rapid eye and head movements (a gaze shift) is commonly used to redirect the visual axes to a new target in space. During gaze shifts, the eye movements produced by the vestibular ocular reflex (VOR) would be counterproductive; the VOR would produce an eye movement commands in the direction opposite to that of the intended shift of gaze. There is now considerable evidence that the VOR is significantly suppressed during gaze shifts. Thus, the head movements generated during gaze shifts contribute to redirecting the axis of gaze relative to space, necessitating the proper coordination of head and eye movements to produce accurate gaze shifts. This talk presents recent results which have shown how the integration of mathematical approaches with traditional neurophysiological tools can provide a coherent view of how the brain coordinates multiple muscles to redirect gaze. This combined approach has been crucial for improving our current understanding the control of eye-head coordination as well as binocular eye movements during gaze shifts.