There is clear evidence that spatial attention increases neural responses to attended stimuli in extrastriate visual areas and, to a lesser degree, in earlier visual areas. Other evidence shows that neurons representing unattended locations can also be suppressed. However, the extent to which enhancement and suppression is observed, their stimulus dependence, and the stages of the visual system at which they are expressed remains poorly understood. Using fMRI we set out to characterize both the task and stimulus dependence of neural responses in the lateral geniculate nucleus (LGN), primary visual cortex (V1), and visual motion area (V5) in humans to determine where suppressive and facilitatory effects of spatial attention are expressed. Subjects viewed a lateralized drifting grating stimulus, presented at multiple stimulus contrasts, and performed one of three tasks designed to alter the spatial location of their attention. In retinotopic representations of the stimulus location, we observed increasing attention-dependent facilitation and decreasing dependence on stimulus contrast moving up the visual hierarchy from the LGN to V5. However, in the representations of unattended locations of the LGN and V1, we observed suppression, which was not significantly dependent on the attended stimulus contrast. These suppressive effects were also found in the pulvinar, which has been frequently associated with attention. We provide evidence, therefore, for a spatially selective suppressive mechanism that acts at a subcortical level.