Weeping Angels are a fictional race of creatures from the Doctor Who universe. They appear to be stone statues, but only when being observed. As a result, they often cover their eyes to avoid looking at each other, thus giving the appearance of "weeping". When unobserved, they can move with incredible speed, often crossing entire rooms in the blink of an eye.
To survive, Weeping Angels require time energy, and their preferred method of gaining it is by sending their victims into the past. By doing this, they can feed on the time potential energy of the life that could have been lived. There has also been an instance of Angels trying to access a TARDIS for energy, and in another instance trying to feed on the spillage from a rip in the space-time continuum.
They can manipulate electrics remotely, and drain power from machinery. This is useful to them in that it allows them to turn out the lights of whatever room they may be in, stopping them from being observed. Additionally, if they desire to communicate with humans they are able to remove part of a victim's brain and reanimate a version of their consciousness, making it say whatever they please.
Fully-powered Weeping Angels can use their image as a weapon. Any image of an Angel (such as the one to the right of this page) is itself an extension of that Angel, and is capable of performing all of the same actions - an Angel can even emerge from a video recording.
Looking directly into an Angel's eyes for too long allows them to imprint their image in your mind. From there the Angel can play havoc with your brain, creating illusions and eventually killing you, although they can be paused in their tracks if you close your eyes.