Visual neuroscience has long sought to determine the extent to which stimulus-evoked activity in visual cortex depends on attention and awareness. Some influential theories of consciousness maintain that the allocation of attention is restricted to conscious representations [1, 2]. However, in the load theory of attention [3], competition between task-relevant and task-irrelevant stimuli for limited-capacity attention does not depend on conscious perception of the irrelevant stimuli. The critical test is whether the level of attentional load in a relevant task would determine unconscious neural processing of invisible stimuli. Human participants were scanned with high-field fMRI while they performed a foveal task of low or high attentional load. Irrelevant, invisible monocular stimuli were simultaneously presented peripherally and were continuously suppressed by a flashing mask in the other eye [4]. Attentional load in the foveal task strongly modulated retinotopic activity evoked in primary visual cortex (V1) by the invisible stimuli. Contrary to traditional views [1, 2, 5, 6], we found that availability of attentional capacity determines neural representations related to unconscious processing of continuously suppressed stimuli in human primary visual cortex. Spillover of attention to cortical representations of invisible stimuli (under low load) cannot be a sufficient condition for their awareness.