A simple mathematical model of the orientation tuning of visual cortical neurons is introduced and analysed. It is shown that the basic cortical architecture of recurrent local excitation and lateral inhibition, together with some feedforward inhibition can account quantitatively for such tuning properties, and their modification by inhibitory blocking agents. The model can also account quantitatively for such local effects as cross-orientation suppression. It is also shown that non-local coupling between iso-orientation patches, when added to the model, can satisfactorily reproduce such effects as non-local iso-orientation suppression, and non-local cross-orientation enhancement. These results will be discussed in relation to cortical development and to a number of perceptual phenomena such as the geometric visual patterns seen following the ingesting of hallucinogens, the "pop-out" effect, and both the direct and indirect tilt illusions.