The hollow-face illusion is one of the most dramatic and robust illusions I’ve ever come across. It’s been known for well over 200 years, but it never ceases to amaze me, as this video demonstrates:
A three-dimensional hollow face mask held a few feet away will appear to be convex (turned “out” towards the viewer) no matter which side you look at (this image is from the Max-Planck-Institut für biologische Kybernetik in Tübingen). While the movie depicts a computer-generated model, the effect works just as well with a real physical mask. Scientists have attempted to explain the illusion for centuries, but there is still much we don’t know about how it works. Our visual system can use tools like binocular disparity and motion parallax to judge distance, but these techniques don’t seem to work with the hollow mask until we’re extremely close to it: for many people, nearer than three feet. The effect is diminished if the mask is turned upside-down, but it doesn’t disappear; nearly everyone still sees the illusion.
The effect isn’t completely due to the direction of lighting either. While the visual system tends to assume light is coming from overhead, hollow masks lit from below still appear convex. Others have suggested that the illusion arises because we “know” that we’re seeing a face, and that knowledge trumps other visual cues that suggest it’s not convex like a real face would be.
If this is true, then the effect should be stronger for more familiar objects, and weaker for less familiar things. Harold Hill and Alan Johnston showed 12 volunteers three different hollow shapes: molds in the form of a teddy bear, a pineapple, and a “jelly mold” (Americans would call this a “jello mold”):

The viewers walked slowly towards each mold (facing away from them) until they could clearly see it “switch” from convex to concave, thus establishing how close they could be and still see the illusion. Here are the results:

As objects became more familiar (and arguably more human-like), people could stand closer and still see the illusion. For both teddy bears and pineapples, the illusion was stronger when they were upright, but for the jello mold, orientation made no difference. The experiment was repeated with a human face, at four different orientations. The upright face had an even stronger effect than the teddy bear, but the illusion was still present when the face was upside-down, and just as strong as the teddy bear.
Next Hill and Johnston moved to computer-generated images of faces. These were displayed stereoscopically, and viewers wore 3-D glasses. This time they systematically modified the faces, gradually adding noise. Here are a few examples:

Fourteen viewers gave each image a convexity rating, ranging from 6 (definitely convex) to 1 (definitely concave). Remember, all the images were rendered to be concave — the cues the 3-D glasses gave them suggested that these were not real faces, but hollow shells. Here are the results:

As more noise was added, making the face look less “real,” viewers were less likely to fall for the illusion, rating it significantly lower on the convexity scale. The illusion persisted longer for color faces than those rendered in gray-scale, again suggesting that the idea that we’re seeing a “real” face makes us more likely to see the face popping out towards us.
All this adds up to a fairly convincing argument that our perception of a face as a whole is what causes us to see the mask as convex, like a real face instead of a hollow shell. Our visual system is receiving a variety of different cues to depth of objects, and prioritizes them in ways that are usually quite accurate. But illusions such as the hollow face demonstrate that those priorities don’t always work. Fortunately we don’t see hollow masks nearly as often as real faces, so for the vast majority of our visual experience, our visual world seems just fine. These anomalies — what we see as illusions — can offer a powerful window into how our visual system actually works.
Hill, H., & Johnston, A. (2007). The hollow-face illusion: Object-specific knowledge, general assumptions or properties of the stimulus? Perception, 36 (2), 199-223 DOI: 10.1068/p5523