In this article we address the major issue of space vision, how the brain represents the 3D shape of objects in the real world, on the basis of psychophysics and neurophysiology. In psychophysics, Gibson found texture gradients and width gradients, as well as the gradient of binocular disparity, as the major cues for surface orientation in depth. Marr proposed that a surface-based representation is the main step towards 3D shape representation. In our neurophysiological studies of the monkey parietal cortex, we have found visual-dominant neurons in area AIP with selectivity in 3D shape of the objects, and also surface-orientation-selective (SOS) neurons in the caudal intraparietal (CIP) area. SOS neurons responded selectively to surface orientation in depth presented in random dot stereograms with a disparity gradient. Many of the SOS neurons responded selectively also to texture gradients and linear perspective, and their responses were enhanced by the combination of these cues. We also found axis-orientation-selective (AOS) neurons in area CIP, responding selectively to the orientation of the longitudinal axis of elongated objects in depth. We present preliminary data here to demonstrate that some of AOS neurons that prefer intermediate thickness are shape-selective, and they are likely to discriminate surface curvature. These data suggest that neurons in and around area CIP may have the capacity to represent 3D shape.