The next topics do not reflect how depth is represented in art but will explore other aspects of how our visual system functions and how that is used in art. The first topic is a general characteristic of our perceptual capabilities: figure-ground perception. It seems that our visual system simplifies the visual scene into a figure that we look at and a ground which is everything else and forms the background. This tendency is exploited in reversible figure-ground figures like at the beginning of this page. It is a coarse rendition of the vase/two faces figure. You can see the drawing as either a central vase, or two faces that are looking at each other. Generally when you see one of the perceptions, the other region forms a background and is not seen, so to see both percepts requires switching back and forth.
M. C. Escher, again, used to take advantage of this characteristic of perception in his art. The picture below "Moebious with Birds has a central region where both white and dark birds are depicted, but only one of the sets of birds tends to be perceived at a time.
Moebius with Birds (detail) by M. C. Escher