A while back Mercedes came out with a fuel cell powered vehicle and decided to promote the concept by creating an invisible car. They draped LED mats on one side of a B-class hatchback and put a camera on the other side, then hooked them together so the camera image could be transmitted live to the LED array on the other side. The end result can be seen in the promotional video below:
I show this to illustrate at least one way to approach a cloaking technology. Absorb the incident light and then re-transmit it on the opposite side in all directions. The reason it doesn't quite work is that light doesn't just pass through an object through its center - it comes at it from every possible angle. As can be seen in the Mercedes clip, the invisible car effect only works in one direction and from a specific distance away, and it requires objects on the camera side to be sufficiently far away. To accomplish the real effect, an object would need to be covered with tiny cameras, each of which could capture video in every direction. It would also be covered with tiny projectors, each of which could transmit (different) video in every direction. All these would need to be connected to a network backbone so that every camera could send real time data to every projector. Even if this mesh of physical equipment could be brought down to nanotech scales, the wiring and bandwidth requirements would render it physically unworkable.
composite materials that can produce negative refraction. So far it's only been done either on a microscopic scale or only in one direction. For larger objects, the problems described above don't go away. Think of it this way - even if you wanted to hide a perfect sphere, there is still a beam of photons traveling between every two points on the sphere in both directions. It is unlikely that any system of angle deflection could handle such a complex problem. I say unlikely only because our understanding of the physics of negative refraction is so new that I can't rule out some new discovery that might actually do the trick. I just wouldn't put money on it.
The writers of Star Trek never really tried to explain how a cloaking device actually worked, and that's generally the way it goes in most of the sci-fi that I've encountered so far. It would be neat to see more attempts at explaining to readers how an invisibility cloak could plausibly become a reality.