Scientists have proposed plans for a kind of Star Trek-style cloaking device: materials that would bend light or other radiation around an area of space, effectively creating an invisibility shield.

The man-made materials are embedded with networks of exceptionally tiny metal wires and loops. The structures refract, or bend, different types of electromagnetic radiation—such as radar, microwaves, or visible light—in ways natural substances can’t.

The theory of metamaterials says that it would be difficult to detect that the light was ever bent around an object; there would not be disturbances revealing that something was being concealed.
Many obstacles stand in the way of practical application. For instance:

So far researchers have only developed metamaterials that divert radar and microwaves—rather than light waves, which are the key to invisibility. While that’s good news for Air Force generals who want to conceal warplanes, it’s bad news for wannabe wizards hoping for a magic cloak. Metamaterials that control visible light are particularly elusive in large part because the required matrix of metal loops and wires must be “nanosize,” or exceptionally small.

The Economist raises an objection on general principle:

Even if it ultimately proved possible to make an aeroplane completely invisible at all wavelengths, there would be a further problem. According to the laws of physics, an invisible person would necessarily be blind. In order to see light, the eye must absorb it, but in order for a person to be invisible, the body must not absorb any light. Thus, a spy plane could not be completely invisible if it were to be used for espionage or, indeed, flown at all, since its pilots would need to know its position relative to the ground.

More here in Book of Joe, especially the comment.