Article suggested by Masumeh, who is researching liquid bifocal and progressive lenses as a treatment for presbyopic (farsighted) patients.

There are several current projects that use Liquid Crystal Displays (LCD) to create magnification lenses. Some of the projects are being developed for use in small cameras such as cell phone cameras. There is also a project that uses the LCD's in a bifocal type of application (see picture).

Here's basically how these liquid lenses work:
There is a layer of Liquid Crystals sandwiched between two pieces of containing material. In the case of liquid bifocals, developed by Nasser Peyghambarian of the University of Arizona, this containing material is two pieces of flat glass. In the case of camera lenses, developed by Varioptic of France and Fraunhofer Institute for Applied Optics and Precision Engineering of Germany, the construction is more complicated and involved sandwiching the LCD between two oil based substrates. These liquid lenses are then placed between plastic lenses of various focal lengths. The liquid lenses and the plastic lenses are used in different configurations to form different total focal lengths (or magnification levels) for the lenses.

Back to basics, in both cases the basic idea is that LCD's are contained between two flat planes. When there is no current applied to the LCD's light will pass directly through the flat containing planes, in other words the LCD is transparent when no power is supplied. When an electric current is supplied to the LCD, the light can be made to bend, this make the liquid lens behave just like a glass lens.

What are the advantages of the liquid lens approach to eyeglasses and cameras?
In the case of cameras, it is potentially cheaper to make a small lens with greater magnification using the technique of liquid lenses. Samsung already incorporates the liquid lens into some of their cellphones. One reason that liquid lenses can be lower cost than conventional zoom lenses is that there are less individual lenses required to create variable focal lengths. Conventional zoom lenses often use 20 or more lenses. A zoom lens of 2.5x magnification using liquid lenses takes only 4 lenses.

In the case of bifocals, using a liquid lens approach resolves the problem of changing image quality across the lens. NPR described it best:

People have to constantly move their eyeballs up and down. For some people, it can make images seem to jump around. And even though newer, "no-line" or progressive bifocals can help with this problem, some people still find that images are blurry at the edges or seem to "swim."

The current simple prototype of the liquid bifocal lens eliminates this problem. However, I think that there is a promise with these liquid lenses which renders them even more useful - the possibility of having lenses which are progressively variable across a range of focal lengths. As your eyes focus either near or far, the lenses automatically change shape to provide proper focus. Mr. Peyghambarian is looking into using a gadget similar to what automatic cameras use to judge distance. However, judging by what the French and German developers of similar cameras lenses have stated, it is easier for the moment to focus on creating liquid lenses that offer a fixed number of focal lengths. The reason is best stated by the New Scientist:

...changing a zoom lens’s magnification also affects its focus, and causes problems such as pincushion distortion and chromatic aberration.

Conventional zooms often require 20 or more lenses - many that move - to preserve image quality across the whole range of magnification, but nobody has come up with a liquid lens design that can do that.

A first step, however, is to design a lens that offers different levels of magnification rather than a continuous range.

Related Links
Abstract of a study using liquid lenses for cameras
New Scientist Tech on liquid lenses for cameras
NPR on liquid lenses for bifocals