This article develops the FACADE theory of 3-dimensional (3-D) vision and figure-ground separation to explain data concerning how 2-dimensional pictures give rise to 3-D percepts of occluding and occluded objects. The model describes how geometrical and contrastive properties of a picture can either cooperate or compete when forming the boundaries and surface representation that subserve conscious percepts. Spatially long-range cooperation and spatially short-range competition work together to separate the boundaries of occluding figures from their occluded neighbors. This boundary ownership process is sensitive to image T junctions at which occluded figures contact occluding figures. These boundaries control the filling-in of color within multiple depth-sensitive surface representations. Feedback between surface and boundary representations strengthens consistent boundaries while inhibiting inconsistent ones. Both the boundary and the surface representations of occluded objects may be amodally completed, while the surface representations of unoccluded objects become visible through modal completion. Functional roles for conscious modal and amodal representations in object recognition, spatial attention, and reaching behaviors are discussed. Model interactions are interpreted in terms of visual, temporal, and parietal cortices.