The presentation below gives an excellent overview of progress in compressive displays. I like to think about them as simply "thick displays", as they involve a stack of components, often more than one layer of LCD filtering and some optical components such as diffusers or micro-lenses.
Such displays can be used to achieve super resolution (apparently finer details than the LCD components should allow) or perspective (different views visible from different angles, for stereoscopy).
For instance, one application which I mentioned before is to get very high contrast displays by using an array of white LEDs as the backlight for an LCD.
Those thick displays not only involve hardware, but also software to drive the different components. For instance, you need to infer the insides of the display (the setting of each pixel in the layers) to achieve the output from a given perspective. This is related to the computed tomography problem, how to produce a volumetric view of the body from projections from various angles.
This paper on cascaded displays is pretty readable and gives a good sense of how you can do that (and the trade-offs involved in brightness and apparent resolution).