Theoretical physicist Michio Kaku discusses the possibility of rendering objects invisible using tiny light-bending materials in this Natural History article.
In order to make an object invisible, visible light needs to be bent around the object. Think of a stream of water flowing around the surface of a stone: water flows around the perimeter until it makes it way completely around that stone and continues along its original path. If the same feat can be done with light rays, that stone would be invisible!
Doing so requires light waves to be bent at extreme angles previously thought impossible. But scientists have synthesized new "metamaterials," that do just that. In 2006, researchers at Duke University and Imperial College London built materials that made objects invisible to microwave radiation.
These metamaterials must be smaller than the wavelengths of the radiation they are bending, so doing the same with visible light is a considerably more difficult feat: while microwaves have a wavelength of 3 centimeters, visible light waves have a wavelength of only a few hundred nanometers. (One nanometer is one billionth of a meter. That's really really small: approximately five atoms fit across one nanometer.)
Developing the nanotechnology required to make invisibility cloaks appear to be researchers' biggest challenge. So scientific teams across the world are currently exploring different methods of refracting red light, since red light has the longest wavelength in the visible spectrum. Whether or not any of these methods succeeds is anybody's guess; but, the ultimate goal is to bend all frequencies of light completely around the object, rendering it invisible. Far out.
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