There is, as yet, no satisfactory theory of stereopsis, despite the fact that our overt knowledge of "solid seeing" is now about 150 years old, and that contributions to our understanding come today from many fields: ophthalmology, psychology, psychophysics, neurophysiology, computer modelling, and optical-TV display technology. We review herein, and demonstrate for the reader whenever possible, certain key perceptual properties of the stereoscopic event of which any general theory must take account: vector stereoscopy and the neural grid, depth in empty visual fields, the relationship between stereoscopic and cognitive contours, stereoscopic contour formation in the presence of blur (thus, at low levels of central visual acuity), the phenomenon of cortical locking and of neural grid evocation in the presence of either peripheral or central rivalry, certain unusual ranges of figural mismatch and the concept of the horopter in relation to modern single cell electroneurophysiology in animals and to the constancy of visual directions. Some comments are also made on the concept of disparity processing by single cortical neurons, together with a short discussion of the implications of certain views of the genetics of stereovision for the perception of novel random texture sine-wave stereograms. We conclude that any theory pertinent to ophthalmology and visual science must combine the global concepts of cortical integration, the neural lock and the neural grid, herein introduced, with the more classical concepts of particulate or local binocular cortical correspondence. Certain preliminary steps in this direction are presented.