Attention enables us to efficiently and flexibly interact with the environment by prioritizing some image features in preparation for responding to a stimulus. Using a concurrent psychophysics- fMRI experiment, we investigated how covert spatial attention affects responses in human visual cortex prior to target onset, and how it affects subsequent behavioral performance. Performance improved at cued locations and worsened at uncued locations, relative to distributed attention, demonstrating a selective tradeoff in processing. Pre-target BOLD responses in cortical visual field maps changed in two ways: First, there was a stimulus-independent baseline shift, positive in map locations near the cued location and negative elsewhere, paralleling the behavioral results. Second, population receptive field centers shifted toward the attended location. Both effects increased in higher visual areas. Together, the results show that spatial attention has large effects on visual cortex prior to target appearance, altering neural response properties throughout and across multiple visual field maps.