A mathematical model of the distal portion of the vertebrate retina has been developed and implemented on a digital computer. With this model, the processing of spatiotemporal visual information through the first layers of retinal neurons can be studied and the functional role of the various cells and intercellular connections discerned. The model, which includes receptor, horizontal, and bipolar cells, summarizes the knowledge obtained from electrophysiological and histological data published in the open literature during the last ten years. Linear and nonlinear characteristics have been incorporated in the form of differential equations and functional expansions (Volterra-Wiener functionals), whichever is deemed preferable in each case. The spatial organization of the neuronal networks is also taken into account. The model duplicates with sufficient accuracy the experimental results obtained by a variety of investigators through stimulus-response data. The study of the functional aspects of this model gives some first suggestions for the development of a rational theory of visual information processing.