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Selective visual attention modulates neural activity in the visual system in complex ways and leads to enhanced performance on difficult visual tasks. Here, we show that a simple circuit model, the stabilized supralinear network, gives a unified account of a wide variety of effects of attention on neural responses. We replicate results from studies of both feature and spatial attention, addressing findings in a variety of experimental paradigms on changes both in firing rates and in correlated neural variability. Finally, we expand this circuit model into an architecture that can perform visual tasks—a convolutional neural network—in order to show that these neural effects can enhance detection performance. This work provides the first unified mechanistic account of the effects of attention on neural and behavioral responses.