Fairy

Fairies, as the human race called them, were dangerous humanoid entities native to the Earth. Fairies were not alien life-forms, but had lived alongside humanity since the dawn of time. Their exact nature was unclear, although Jack Harkness described them as part myth, part spirit world and part reality jumbled together, mixed with "old moments and memories". He speculated that they might be "part Mara". Though incredibly dangerous and capable of wiping out humanity, they were not a direct threat unless they or their so-called "Chosen Ones" were explicitly harmed or threatened. There was no way to trap them as they controlled the elements of Fire, Earth, Air and Water. (TV: Small Worlds)

According to the Twelfth Doctor, Fairies were also called "the Fae", "the Fair Folk" and "Homo fata vulgaris". They came from the Invisible, a realm that ran alongside Earth. (PROSE: The Shining Man)

Biology
Fairies had a wide variety of advanced, seemingly magical abilities. They had control over the elements and could produce localised, deadly storms and gales. Not bound by normal physical laws, they could choose whether a camera could take their pictures. They made themselves invisible to closed circuit television cameras on one occasion. On another, they let their photographs be taken. They could travel through time and had an apparently non-linear relationship to it; a picture of Jasmine Pierce, who became a Fairy in the 21st century, was seen in her fairy form in 1917. They could kill their victims by "stealing their breath", asphyxiating them by clogging their throats with rose petals, drowning them via rainstorms or using gales to draw all oxygen away from the victim. One was also somehow able to get into and out of a fully sealed police cell without disturbing anything.

Fairies could be seen in two forms: a small, glowing humanoid form with butterfly-like wings; and a human-sized, more monstrous form. Both forms had wings and could fly with ease. At least in the larger form, Jack Harkness described them as only visible from the corner of one's eyes. (TV: Small Worlds)

History
Jack Harkness told Gwen Cooper that Fairies came from the Dawn of Time. Humans, over time, made Fairies into something harmless and beautiful, but those who had encountered them, like Jack, never doubted their powers. (TV: Small Worlds)

When the Earth was young, the veil between the Invisible and the Visible was thinner, allowing fairies to cross the divide and wreak havok in the human dimension. They frequently attacked Huckensall village. The people in the village protected themselves by building the doors in the village from the wood of a rowan tree. In 1654, a Fairy Finder came to the village and rounded up the Fae, burying them deep in the ground. (PROSE: The Shining Man)

According to Jack, Fairies were once human children taken from various times stretching millennia into the past. These children were called the Chosen Ones, whom the Fairies protected and avenged if harm came to them. Eventually, the Fairies would claim these children and take them to their "Lost Lands". Once there, the children would become Fairies themselves. The Fairies required these children to continue their race, despite being immortal (or near-immortal). These "Chosen Ones" always seemed slightly odd and would try to spend as much time as possible with the Fairies.

The Fairies were not generally involved with the affairs of other humans, but they violently defended any infringements on their territory and killed anyone they felt had acted against them. Despite this, they did not kill two girls who were bullying Jasmine Pierce, possibly indicating an unwillingness to harm children.

They could also distinguish between those who harmed the Chosen child and who didn't. When Jack was on a train with a group of soldiers who had run over a Chosen One, the fairies attacked the men, but left Jack unharmed in a car full of dead bodies. The Fairies also appeared to have limitless powers over the elements. Jasmine Pierce, a Chosen One, told the team, when they tried to stop her being taken, that they would "turn the world to ice". When Jack said that would mean no more Chosen Ones, Jasmine said the Fairies would simply keep to the past. (TV: Small Worlds)

In 2017, the Shining Man craze on the internet led to a general sense of fear among the public, and the barriers between the Invisible and the Visible began to weaken, allowing fairies to interact with humans again. (PROSE: The Shining Man)

The Eighth Doctor encountered a species called the Sidhe, which was also immortal and able to move through time, and also said to be responsible for the Earth legends of fairies. (PROSE: Autumn Mist)

The Doctor encountered fairies alongside Madame Vastra during his ninth (or earlier) incarnation. (COMIC: The Lost Dimension)