The dorsal convexity of the human frontal and parietal lobes forms a network that is crucially involved in the selection of sensory contents by attention. This network comprehends cortex along the intraparietal sulcus, the inferior parietal lobe, and dorsal premotor cortex, including the frontal eye field. These regions are richly interconnected with recurrent fibers passing through the superior longitudinal fasciculus. The posterior parietal cortex has several functional characteristics-such as feature-independent coding, enhancement of activity by attention, representation of task-related signals, and access to multiple reference frames-that point to a central role of this region in the computation of a feature- and modality-independent priority map of the environment. The priority map integrates feature information elaborated in sensory cortex and top-down representations of behavioral goals and expectations originating in the dorsolateral prefrontal and premotor cortex. This review presents converging evidence from single-unit studies of the primate brain, functional neuroimaging, and investigations of neuropsychological disorders such as Bálint syndrome and spatial neglect for a decisive role of the frontoparietal attention network in the selection of relevant environmental information.