This article provides a systems framework for the analysis of cortical and subcortical interactions in the control of saccadic eye movements, A major thesis of this model is that a topography of saccade direction and amplitude is preserved through multiple projections between brain regions until they are finally transformed into a temporal pattern of activity that drives the eyes to the target. The control of voluntary saccades to visual and remembered targets is modeled in terms of interactions between posterior parietal cortex, frontal eye fields, the basal ganglia (caudate and substantia nigra), superior colliculus, mediodorsal thalamus, and the saccade generator of the brainstem. Interactions include the modulation of eye movement motor error maps by topographic inhibitory projections, dynamic remapping of spatial target representations in saccade motor error maps, and sustained neural activity that embodies spatial memory. Models of these mechanisms implemented in our Neural Simulation Language simulate behavior and neural activity described in the literature, and suggest new experiments.