Somewhere between the retina and our conscious visual experience, the majority of the information impinging on the eye is lost. We are typically aware of only either the most salient parts of a visual scene or the parts that we are actively paying attention to. Recent research on visual neurons in monkeys is beginning to show how the brain both selects and discards incoming visual information. For example, what happens to the responses of visual neurons when attention is directed to one element, such as an oriented colored bar, embedded among an array of other oriented bars? Some of this research shows that attention to the oriented bar restricts the receptive field of visual neurons down to this single element. However, other research shows that attention to this single element affects the responses of neurons with receptive fields throughout the visual field. In this review, these two seemingly contradictory results are shown to actually be mutually consistent. A simple computational model is described that explains these results, and also provides a framework for predicting a variety of additional neurophysiological, neuroimaging and behavioral studies of attention.