A gaze-stabilization reflex that has been conserved throughout evolution is the rotational vestibuloocular reflex (RVOR), which keeps images stable on the entire retina during head rotation. An ethological newer reflex, the translational or linear VOR (TVOR), provides fast foveal image stabilization during linear motion. Whereas the sensorimotor processing has been extensively studied in the RVOR, much less is currently known about the neural organization of the TVOR. Here we summarize the computational problems faced by the system and the potential solutions that might be used by brain stem and cerebellar neurons participating in the VORs. First and foremost, recent experimental and theoretical evidence has shown that, contrary to popular beliefs, the sensory signals driving the TVOR arise from both the otolith organs and the semicircular canals. Additional unresolved issues include a scaling by both eye position and vergence angle as well as the temporal transformation of linear acceleration signals into eye-position commands. Behavioral differences between the RVOR and TVOR, as well as distinct differences in neuroanatomical and neurophysiological properties, raise multiple functional questions and computational issues, only some of which are readily understood. In this review, we provide a summary of what is known about the functional properties and neural substrates for this oculomotor system and outline some specific hypotheses about how sensory information is centrally processed to create motor commands for the VORs.