The Silence

The Silence were a mysterious species that forced the Doctor's TARDIS to explode on the date of June 26th 2010, and thus created cracks in time that would erase various things throughout the universe, and eventually the universe itself.

Biology
The Silence were tall humanoids with bulbous heads and grey, mouthless faces. Their hands possessed large, elongated fingers with a bulbous central finger. They spoke in low, guttural voices and tended to make growling or clicking noises. (DW: The Impossible Astronaut)

Powers and abilities
The Silence were able to remain hidden on Earth, as anyone who saw them would instantly forget about them the moment they looked away. Someone looking at the Silence would recover their memories of previous sightings (though not instantaneously). In addition, the Silence seemed to be able to physically move from place to place very quickly.

The Silence could also use an energy discharge from their hands to kill and obliterate someone, leaving only ashes behind. It appeared that they had to draw this energy from an outside source though, as when performing this act the energy from the lights flew into it. When absorbing the energy and discharging it, a hole appeared where a mouth should have been. (DW: The Impossible Astronaut, Day of the Moon)

They could also influence humans by saying something while a person was looking at them, which would remain in there heads after they looked away in a form of post-hypnotic surgesion. Constantly doing this would cause the person in question to lose their mind. (DW: Day of the Moon)

History
The Silence first took control of the Doctor's TARDIS in 102 A.D. They forced it to land outside of Amy Pond's house on June 26th 2010, and it exploded shortly afterward, trapping River Song inside it within a time loop until the Doctor saved her. Although the entity behind the voice was never visible or named, it was heard speaking before the TARDIS exploded, saying: "Silence will fall!" (DW: The Pandorica Opens / The Big Bang). In 1580 Venice, Rosanna Calvierri said that through some of the cracks, the Saturnynians saw only silence and the end of all things. This caused them to flee their homeworld to Earth. (DW: The Vampires of Venice)

The Silence were apparently present on Earth for hundreds of years, going unnoticed by the human race. One of them spied on the Doctor, Amy, Rory, and River in Utah, 2011. Another one visited the White House in 1969 and killed Joy in front of Amy Pond. (DW: The Impossible Astronaut) The Silence were defeated by the Doctor when he ensured humanity saw footage of a Silent ordering people to kill them on sight. This 'command' acted like a post-hypnotic suggestion and resulted in the human race finally turning on the Silence. (DW: Day of the Moon)

Behind the scenes

 * Marnix Van Den Broeke portrayed the Silence in The Impossible Astronaut.
 * Moffat states that he was inspired by Edvard Munch's The Scream when creating the Silence's appearance.
 * Their appearance and method of operation, as well as ability to be forgotten easily all seem to bear similarity to the real life stories of the Grey aliens.