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Context is known to affect how a stimulus is perceived. A variety of illusions have been attributed to contextual processing—from orientation tilt effects to chromatic induction phenomena, but their neural underpinnings remain poorly understood. Here, we present a recurrent network model of classical and extraclassical receptive fields that is constrained by the anatomy and physiology of the visual cortex. A key feature of the model is the postulated existence of near- versus far- extraclassical regions with complementary facilitatory and suppressive contributions to the classical receptive field. The model accounts for a variety of contextual illusions, reveals commonalities between seemingly disparate phenomena, and helps organize them into a novel taxonomy. It explains how center-surround interactions may shift from attraction to repulsion in tilt effects, and from contrast to assimilation in induction phenomena. The model further explains enhanced perceptual shifts generated by a class of patterned background stimuli that activate the two opponent extraclassical regions cooperatively. Overall, the ability of the model to account for the variety and complexity of contextual illusions provides computational evidence for a novel canonical circuit that is shared across visual modalities.