The mathematics of cloaking. One interesting tidbit:

Their analysis also revealed another surprise: a person trying to look out of the cloak would effectively be faced with a mirror in every direction. If you can imagine Harry Potter's own invisibility cloak working this way, and Harry turning on his flashlight to see, its light would shine right back at him, no matter where he pointed it.

And from the University of Rochester press release:

The current work of Greenleaf, Kurylev, Lassas, and Uhlmann mathematically proves full-wave invisibility of active devices at all frequencies -- if suitable modifications are made to the original constructions.

Rather than cloaking an inactive object, which does not generate EM waves, the new mathematics allows for cloaking active devices, such as cell phones, computers, and anything else that might generate signals. In addition, the mathematics works (theoretically) at all wavelengths.

Here's some background information.