The Weeping Angels are a group of psychopathic hunters featured in the Tenth Doctor episode "Blink". Because their physiology is quantum-locked (see Schrödinger's Cat), they turn to stone when observed, covering their eyes with their hands and arms to prevent themselves looking at each other: this gives the impression that they are 'weeping'. This acts as a defence mechanism; they cannot be killed while petrified (though equally they cannot kill). They can move with great speed, being fast enough to move across a street in a single blink of the eye.
According to the Doctor, the Angels are as old as the universe (or very nearly) but no one really knows where they come from. He also describes them as "creatures of the abstract", "the lonely assassins", and "the only psychopaths in the universe to kill you nicely", because their method of "killing" doesn't do anything of the sort: a touch sends their victims into the past to live out their lives before they were even born; the Angels then feed on the "potential energy" of the lives their victims would have lived in the present.
In "Blink", a quartet of Weeping Angels strand the Doctor and his companion Martha Jones in the year 1969, and attempt to feed off the vast potential energy reserves of the TARDIS. Despite dispatching the Doctor, the Angels fail to get into the TARDIS; though they get the key, they can't find the machine itself. Sally Sparrow takes the key from one of them while it is in stone form, leading them to stalk Sally to regain it. During their pursuit, Sally inadvertently leads them to the TARDIS. Eventually the four Angels, having surrounded the TARDIS, are tricked into looking at each other when the box disappears, leaving them locked in their stone forms.