The Silence

 was a religious order. Their core belief was that "silence will fall when the Question [was] asked" — "the Question" being the first Question of the universe. The Question itself is unknown.

Beyond this core belief was the significant goal of killing the Doctor, whom the Silence felt interfered with their central tenets. (DW: Let's Kill Hitler)

The order and the Doctor
The Silence made many attempts upon the Doctor's life. It was they that forced the Doctor's TARDIS to explode on 26th June 2010, creating cracks in time that would erase things throughout the universe, and eventually the universe itself. It is not known if the destruction of the universe was actually part of the Silence's plan. 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)

The Silence played a hand in the destruction of the Saturnynian's homeworld. 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)

The Silence were also behind the Battle of Demons Run, as well as the kidnapping and brainwashing of a young River Song. She then made several attempts on the Eleventh Doctor's life. Ultimately, she successfully introduced a poison into his system which would most certainly have killed him, had she not broken free of her conditioning and offered him the sum of her regenerative energy. (DW: Let's Kill Hitler)

The Silence as a species
One species associated with the Silence were tall humanoids with bulbous heads and grey, mouthless faces. Their hands had 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)

The true name of this particular species has not been revealed.

Powers and abilities
This species 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 one of the members of the species, the lights in the restroom flickered. 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 others 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 would also happen if the suggestion was made by someone other than "the Silence" to a person looking at an individual of the species 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 of the species
"The Silence" had 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 doing their bidding in such things as going to the moon. (DW: The Impossible Astronaut / Day of the Moon)

A single member of the species spied on the Doctor, Amy, Rory, and River in Utah in 2011, briefly being noticed by Amy before Rory distracted her. Another individual 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 was. They used post-hypnotic suggestion to control the man that had run it into thinking the orphanage was still in operation. They showed great interest in the welfare of the little girl, putting her in the life support "astronaut" suit to keep her healthy and safe - even equipping the suit with a built-in weapons system. The Silence also kidnapped Amy 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 individual member of the species they held captive, spliced into the footage of the moon landing broadcast. In it, the individual said, "You should kill us all on sight". This footage was viewed by 500 million humans live, and would be seen everytime someone viewed the Apollo 11 footage in the future. Humanity began to exterminate the alien species as commanded. Those individuals 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 remainder of the species on Earth in 1969 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.