Silent

The Silents were a "memory-proof" alien species who led a religious order known as the Silence.

Appearance
They were tall humanoids, around seven foot tall, with bulbous heads and grey, mouthless faces. Their hands had four large, spatulate fingers. 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 made growling or clicking noises. For unknown reasons, they wore black suits and ties in the style of 20th century male government workers on Earth. (DW: The Impossible Astronaut/Day of the Moon)

Amnesia and hypnotic ability ability
The Silents remained hidden on Earth for hundreds of thousands of years, since the early Stone Age. They had the unique ability to be "memory-proof"; anyone who saw them would instantly forget about them the moment they looked away - even if they saw a photograph or recording of the Silence. Anyone looking at the Silents would recover their memories of previous sightings, although not instantaneously. The Silents were also impervious to at least some types of scanning devices, as River Song's bio scanner couldn't detect them in the underground tunnels. (DW: The Impossible Astronaut)

The Silents influenced the actions of others by issuing commands to anyone looking at them. These orders would remain in a person's mind after they forgot the encounter with the Silent, acting like post-hypnotic suggestions. Any instruction spoken while a subject looked at a Silent, even a picture of one, would cause this effect. People could be driven insane by having too many orders implanted in this manner. (DW: Day of the Moon)

The Silents employed human or humanoid operatives who wore eye drives, devices worn over the eye that artificially recorded information and fed it directly into the brain, allowing those wearing them to remember the aliens after looking away. (DW: The Wedding of River Song)

Other powers
Silents could also absorb electricity, even the tiniest static electricity from the air, into their bodies, increase the voltage a hundred folds and fire it from their hands. These energy discharges could utterly obliterate victims. When absorbing and discharging energy, a hole would appear where a mouth would be on the Silent's face. (DW: The Impossible Astronaut / Day of the Moon)

The Silents were very strong, able to shatter reinforced glass by merely pushing on it. They could also smash through barricaded doors with ease. One Silent took two direct hits from a handgun at point-blank range and survived, though it was unable to walk. However, Silents can be killed by enough gunfire, as shown when in an alternate timeline, Amy Pond was able to kill three with a machine gun. They can also be killed by a single, direct hit from an energy weapon (such as River Song's Alpha Meson blaster). (DW: Day of the Moon, The Wedding of River Song)

They could hang upside down from ceilings and lie in waiting, much like bats. (DW: The Impossible Astronaut/Day of the Moon, DW: The Wedding of River Song)

History
The Doctor described them as parasites as they were unable to develop any science or technology on their own. Instead they relied on other species. (DW: Day of the Moon)

The Silents had been present on Earth for thousands of years, since the time the wheel and fire were developed, unnoticed by the human race. They used post-hypnotic suggestion to make humans do their bidding in such things as going to the Moon. (DW: Day of the Moon)

Various Silents appeared in London 1605, while Amy, Rory and the Doctor were solving the mystery that involved the Rutan gunpowder plot. At least one Silent was in the Houses of Parliament when it was in orbit. It was seen by Rory Williams whilst he was fixing an EMP generator. (VG: The Gunpowder Plot)

A Silent was in the White House in 1969 (WC: Prequel (The Impossible Astronaut)) and killed a woman named 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)

Before July in 1969, a great number of Silents had taken up residence at a disused orphanage where the little girl was held. They used post-hypnotic suggestions to make the director believe the orphanage was still in operation. They showed great interest in the little girl, putting her in a life support "astronaut" suit to keep her healthy and safe - even equipping the suit with a built-in weapons system. The Silents 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 Silents 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"; it had said this to Canton Delaware, sneering at human mercy while he tried to help heal it after it had been shot. This footage was immediately viewed by half a billion humans, and would be seen every time anyone saw the Apollo 11 landing, one of the most famous and frequently viewed film sequences in the history of humanity. Without enough time to implant more post-hypnotic suggestions when humans looked at them, the remainder of the Silents on Earth in 1969 seemed doomed, although at least one did survive to 2011. (DW: Day of the Moon)

A single Silent survived long enough to spy on the Doctor, Amy, Rory, and River in 2011 Utah, briefly noticed by Amy before she was distracted. (DW: The Impossible Astronaut)

Two Silents witnessed Madame Kovarian kidnap River Song from the Luna University and force her into an astronaut suit as part of Kovarian's plan to kill the Doctor. When River asked Kovarian what they were, Kovarian replied, "your owners." (DW: Closing Time)

In the Area 52 Pyramid in an alternate timeline, over a hundred Silents were "captured" by Amy Pond's troops and placed in specimen tanks filled with water to prevent them from drawing electricity. (WC: Prequel) This turned out to be a trap to get to the Doctor, and the Silents easily broke out and killed the guards. Three Silents then attempted to kill Rory, but were gunned down by Amy. (DW: The Wedding of River Song)

Behind the scenes

 * Steven Moffat has stated that he was inspired by Edvard Munch's The Scream when creating the Silence's appearance. He has also cited that the urban legends of the Men In Black, had inspired him to have Silents wear a black suit and tie.
 * Silents appear in the Doctor Who video game The Gunpowder Plot as Easter Eggs. They have no effect on the plot and narrate various in-game descriptions of objects found in the game, often with their own particular spin on them. (VG: The Gunpowder Plot)
 * A single member of the species is known as a "Silent" while more than one are called "Silents". Until clarified in Let's Kill Hitler, the Silents were presumed to be synonymous with the Silence. The Wedding of River Song establishes that the Silents are the leaders of the Silence. Whether "Silents" is indeed the name of the species, or simply a name applied to them by their followers is, to date, unknown.

The Brilliant Book 2012

 * The Brilliant Book 2012, an out-of-Universe REF book, included a lot of unknown history behind the Silence, including:
 * Amy Pond theorised that the Silents created the tribal belief that cameras steal one's soul and were behind the "Maury Island Incident" in 1947. (REF: The Brilliant Book 2012)
 * River Song theorised that the Silents may also have been responsible for the Philadelphia Experiment and had encouraged wars as a form of population control. (REF: The Brilliant Book 2012)
 * Rory Williams thought the rise of 1950s alien invasion films and 1940s-60s UFO sightings might have been subconscious reactions to the Silents and that the Silents made repeated thefts of Edvard Munch's The Scream to suppress imagery of them. (REF: The Brilliant Book 2012)
 * In 1955, people in and around the Kelly-Hopkinsville farmhouse experienced lights and sound, but only a few alledged to seeing aliens. After interviewing witnesses, Air Force Division man Gary F. Hodson drew what people claimed to have seen: a creature that resembled a Silent. (REF: The Brilliant Book 2012)