Anatomical superposition of the cortical projections from the overlapping visual fields of the two eyes does not make it obvious how the disposition of objects in the third dimension is encoded. Hubel and Wiesel's demonstration that units in the primary visual cortex of the mammal respond preferentially to elongated contours of specific orientation encouraged the inquiry into whether binocular disparity might not similarly be represented as an attribute interdigitated within the orderly progression of position. When this was found to indeed be the case, this entrained a brisk research activity into the disparity of receptive fields of single units in the primary visual cortex and the influence on their response of the three-dimensional locations of outside world stimuli. That cells' preferred orientations covered the whole gamut whereas space perception required only horizontal disparity was an apparent paradox that needed resolution. A connection with an observer's stereoscopic performance was made by the discovery that cells in the primate primary visual cortex display good tuning to the disparity in random-dot stereograms. But a wide gap still remains between the properties of these cortical units and human stereo thresholds in simple target configurations, let alone depth judgments in which perceptual and cognitive factors enter. When the neural circuits in the primary visual cortex that are involved in processing depth are eventually traced in detail they will also need to have properties that allow for the plasticity in learning and experience.