The Silence

The Silence were a religious cult that forced the Doctor's TARDIS to explode on 26th June 2010, creating cracks in time that would erase various things throughout the universe, and eventually the universe itself. They acted as parasites, using post-hypnotic suggestion to have other races construct things for them. Their main belief is that after the oldest question in the universe is asked silence will fall.

Biology
The Silence were tall humanoids with bulbous heads and grey, mouthless faces. Their hands possessed four large, elongated fingers with one bulbous central finger. They had small eyes in deep recesses in the skull. The eyes lacked sclera and were completely dark. They spoke in low, guttural voices and tended to make growling or clicking noises. They wore black suits and ties. (DW: The Impossible Astronaut/Day of the Moon) The Silence would also hang upside down from ceilings while they slept, much like Earth bats. (DW: Day of the Moon)

Powers and abilities
The Silence were able to remain hidden on Earth for thousands of years, as anyone who saw them - 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.

The Silence could use an energy discharge from their hands to kill and obliterate humanoid beings, leaving only a little ash. It appeared that they had to draw this energy from an outside source since when Joy was killed by a Silent, the lights in the restroom were flickering on and off. When absorbing energy and discharging it, a hole appeared where a mouth would have been on a human's face. (DW: The Impossible Astronaut / Day of the Moon)

The Silence could influence the actions of other species by ordering any person who looked at them. Any command would remain in a person's mind and take the form of post-hypnotic suggestion. This also worked if the suggestion was made by someone other than a Silent to a person looking at a Silent or an image of one. People could be driven insane by having too many orders implanted by the Silence. (DW: Day of the Moon)

History
The Silence were a religious order, not a species, who believed that 'Silence will fall' when a particular question is asked, the oldest question in the universe, somehow related to the Doctor.

The Silence had apparently been present on Earth for thousands of years, since the time the wheel and fire were developed, going unnoticed by the human race. They used their ability of post-hypnotic suggestion to guide humans into unconsciously doing their bidding in such things as going to the moon. (DW: The Impossible Astronaut / Day of the Moon)

Although the entity that caused the Doctor's TARDIS to explode was never visible or named, a voice was heard speaking before the TARDIS began exploding, 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 1580 Earth through a different crack that acted like a wormhole. (DW: The Vampires of Venice) A Silent spied on the Doctor, Amy, Rory, and River in Utah, 2011, briefly being noticed by Amy before Rory distracted her. Another Silent visited the White House in 1969 and killed Joy in front of Amy Pond before delivering a post-hypnotic suggestion for her to "tell the Doctor what he must know and what he must never know". (DW: The Impossible Astronaut)

At some point, the Silence had taken up residence at a disused orphanage where the little girl had come from and used post-hypnotic suggestion to control the man that had run it previously into thinking the orphanage was still in operation. They showed such interest in the welfare of the little girl, as they put her in the life support astronaut suit to keep her healthy and safe - even going so far as to equip the suit with a built-in weapons system. The Silence later kidnapped Amy for unknown purposes when she was investigating the orphanage with Canton. They took her to their underground lair and cryptically told her that she would help "bring the silence."

The Doctor inflicted a crushing defeat on the Silence when he ensured that humanity saw footage of a wounded Silent they held captive, spliced into the footage of the moon landing broadcast. In it, the Silent said "You should kill us all on sight". This footage was viewed by half-a-billion humans at the time, and would be invariably viewed by their descendants. This sealed the fate of the Silence; humanity began to exterminate Silence as commanded. The group of Silence holding Amy captive tried to kill the Doctor for this. However, River killed all the Silence that were present. Without enough time to implant more post-hypnotic suggestions when humans look at them, the remaining Silence seemed doomed. (DW: Day of the Moon)

Behind the scenes

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