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.

They have been described by the Doctor and River Song to be "parasites" - using post-hypnotic suggestions to get other races to build things for them.

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 for thousands of years, as anyone who saw them - or even a photograph or recording of them - would instantly forget about them the moment they looked away. Anyone looking at the Silence would recover their memories of previous sightings, although not instantaneously. Additionally, 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 a human being, 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 their minds after they looked away in a form of post-hypnotic suggestion. Constantly doing this would cause the person in question to lose their mind. (DW: Day of the Moon)

History
The Silence were apparently present on Earth for hundreds of years since the time the wheel and fire were developed, going unnoticed by the human race. (DW: The Impossible Astronaut/Day of the Moon)

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)

One of the Silence 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) They later kidnapped Amy for unknown purposes and cryptically told her that she would help "bring the silence." (DW: Day of the Moon)

The Silence were defeated by the Doctor when he ensured humanity saw footage of a Silent broadcasted via the moon landing, in which the Silent said the words "You should kill us on sight". Because the Apollo 11 moon landing footage was some of the most famous of all time, viewed at some point by every living human from that point in history on, this 'command' acted like a post-hypnotic suggestion and resulted in the human race finally turning on the Silence - without consciously knowing it. (DW: Day of the Moon)

Behind the scenes

 * Moffat states that he was inspired by Edvard Munch's The Scream when creating the Silence's appearance.