The Silence

For the species identified as the leaders of "The Silence", see Silent.

The Silence was a religious order who considered themselves the “Sentinels of History”. They tried to kill the Doctor because of a specific prophecy, which stated: “On the fields of Trenzalore, at the fall of the eleventh, when no living creature can speak falsely or fail to answer, a Question will be asked, a question that must never, ever be answered.”

This question was “The First Question, the oldest question in the Universe, that must never be answered, hidden in plain sight.” Dorium Maldovar told the Eleventh Doctor that the question was: “Doctor Who?”, which was a question the Doctor had been apparently running from his entire life/lives.

Organisation
The Silence was led by a race of memory-proof aliens (known also as the Silence) who used post-hypnotic suggestion to manipulate other species into doing their bidding. These aliens also employed human or humanoid agents to carry out specific tasks. These agents were often fitted with Eye Drives which allowed them to remember the Silence.

History
The Silence allied with Madame Kovarian, the Church and the Order of the Headless. They were behind the Battle of Demon's Run and the kidnapping and brainwashing of the infant River Song, then known as Melody Pond. She later made several attempts on the Eleventh Doctor's life. Ultimately, she kissed him with poisoned lipstick. She later broke free of her conditioning and offered him the total of her regenerative energy, saving him. (DW: Let's Kill Hitler).

The alien leaders of the Silence were encountered by the Doctor in 1969 America. The Silence had been on Earth since the Stone Age, secretly manipulating humanity for their own ends. (DW: Day of the Moon)

It was implied they were responsible for the Moon landing because they needed a special spacesuit for Melody Pond. The Silence's occupation of Earth was broken when the Doctor issued a post-hypnotic command via the Apollo 11 footage to the entire human race, instructing them to kill the Silents on sight. (DW: Day of the Moon)

The Silence tracked down River Song to the Luna University, where they kidnapped her and forced her into an astronaut suit as part of their plan to kill the Doctor. (DW: Closing Time). One was present near Lake Silencio in Utah to observe the Doctor, River, Amy and Rory during the events of the Doctor's death. (DW: The Impossible Astronaut) Their plan was foiled when the Doctor convinced the crew of the Teselecta to disguise their ship as him and take his place, tricking the Silence into believing they had killed the Doctor at a fixed point in time. The fixed point was rather, the Teselecta's destruction and the deception itself. (DW: The Wedding of River Song)

Behind the scenes
According to The Brilliant Book 2012, a non-canonical REF book; River Song, Rory Williams and Amy Pond would theorise that the Silence may also be responsible for the Philadelphia Experiment and had encouraged wars as a form of population control, as well as creating the tribal belief that cameras would steal one's soul and causing the repeated thefts of Edvard Munch's The Scream to suppress imagery of them. Rory thought the rise of 1950s alien invasion films and 1940s-60s UFO sightings might have been a subconscious reaction to the Silence.