In the monkey brain, two interconnected cortical areas have distinctive neuronal responses to visual, tactile, and auditory stimuli. These areas are the ventral intraparietal area (VIP) and a polysensory zone in the precentral gyrus (PZ). The multimodal neurons in these areas typically respond to objects touching, near, or looming toward the body surface. Electrical stimulation of these areas evokes defensive-like withdrawing or blocking movements. These areas have been suggested to participate in a range of functions including navigation by optic flow, attention to nearby space, and the processing of object location for the guidance of movement. We suggest that a major emphasis of these areas is the construction of a margin of safety around the body and the selection and coordination of defensive behavior. In this review, we summarize the physiological properties of these brain areas and discuss a range of behavioral phenomena that might be served by those neuronal properties, including the ducking and blocking reactions that follow startle, the flight zone of animals, the personal space of humans, the nearby, multimodal attentional space that has been studied in humans, the withdrawal reaction to looming visual stimuli, and the avoidance of obstacles during self-motion such as locomotion or reaching.