Research in neuroscience reveals that the brain constructs multiple representation of space. Here, we primarily focus on peripersonal space (PPS) representation, the region of space immediately surrounding our bodies and in which objects can be grasped and manipulated. We review convergent results from several generations of studies, including neurophysiological studies in animals, neuropsychological investigations in monkeys and brain-damaged patients with spatial cognition disorders, as well as recent neuroimaging experiments in neurologically normal individuals. Collectively, these studies show that the primate brain constructs multiple, rapidly modifiable representations of space, centered on different body parts (i.e., hand-centered, head-centered, and trunk-centered), which arise through extensive multisensory interactions within a set of interconnected parietal and frontal regions. PPS representations are pivotal in the sensory guidance of motor behavior, allowing us to interact with objects and, as demonstrated by recent studies, with other people in the space around us.