Visuospatial cognition requires taking into account where things are relative to each other and not just relative to the viewer. Consequently it would make sense for the brain to form an explicit representation of object-centered and not just of ego-centered space. Evidence bearing on the presence and nature of neural maps of object-centered space has come from two sources: single-neuron recording in behaving monkeys and assessment of the visual abilities of human patients with hemispatial neglect. Studies of the supplementary eye field of the monkey have revealed that it contains neurons with object-centered spatial selectivity. These neurons fire when the monkey has selected, as target for an eye movement or attention, a particular location defined relative to a reference object. Studies of neglect have revealed that in some patients the condition is expressed with respect to an object-centered and object-aligned reference frame. These patients neglect one side of an object, as defined relative to its intrinsic midline, regardless of its location and orientation relative to the viewer. The two sets of observations are complementary in the sense that the loss of neurons, such as observed in the monkey, could explain the spatial distribution of neglect in these patients.