The visual neurosciences have made enormous progress in recent decades, in part because of the ability to drive visual areas by their sensory inputs, allowing researchers to reliably define visual areas across individuals and across species. Similar strategies for parceling higher-order cortex have proven elusive. Here, using a novel experimental task and nonlinear population receptive field modeling we map and characterize the topographic organization of several regions in human frontoparietal cortex. We discover maps of both polar angle and eccentricity that are organized into clusters, similar to visual cortex, where multiple maps of polar angle of the contralateral visual field share a confluent fovea. This is striking because neural activity in frontoparietal cortex is believed to reflect higher-order cognitive functions rather than external sensory processing. Perhaps the spatial topography in frontoparietal cortex parallels the retinotopic organization of sensory cortex to enable an efficient interface between perception and higher-order cognitive processes. Critically, these visual maps constitute well-defined anatomical units that future study of frontoparietal cortex can reliably target.