The activity of the cerebral cortex is thought to depend on the precise relationship between synaptic excitation and inhibition. In the visual cortex, in particular, intracellular measurements have related response selectivity to coordinated increases in excitation and inhibition. These measurements, however, have all been made during anaesthesia, which strongly influences cortical state and therefore sensory processing. The synaptic activity that is evoked by visual stimulation during wakefulness is unknown. Here we measured visually evoked responses--and the underlying synaptic conductances--in the visual cortex of anaesthetized and awake mice. Under anaesthesia, responses could be elicited from a large region of visual space and were prolonged. During wakefulness, responses were more spatially selective and much briefer. Whole-cell patch-clamp recordings of synaptic conductances showed a difference in synaptic inhibition between the two conditions. Under anaesthesia, inhibition tracked excitation in amplitude and spatial selectivity. By contrast, during wakefulness, inhibition was much stronger than excitation and had extremely broad spatial selectivity. We conclude that during wakefulness, cortical responses to visual stimulation are dominated by synaptic inhibition, restricting the spatial spread and temporal persistence of neural activity. These results provide a direct glimpse of synaptic mechanisms that control sensory responses in the awake cortex.