Child

Children, at least in the case of humans, were those individuals who had not yet reached puberty. Sontarans referred to children as half forms. (TV: The Last Sontaran, Enemy of the Bane)

The Timeless Child, later known as the Doctor, came from another realm, and was discovered by the Shobogan explorer Tecteun. They became a genetic template for other Time Lords that could regenerate. (TV: The Timeless Children) At least some Time Lords on Gallifrey also had childhoods, (TV: The Sound of Drums, The End of Time) as did River Song, a human who attained Time Lord DNA at least partially from being conceived in the Doctor's TARDIS. (TV: A Good Man Goes to War) The Tenth Doctor counted 2.47 billion children living on Gallifrey at the end of the Last Great Time War. (TV: The Day of the Doctor)

Children were a necessary part of the Krillitanes plot to crack the Skasis Paradigm, as adults lacked the imagination required to solve it; the Tenth Doctor described it as akin to using the children's souls. (TV: School Reunion)

In a dream, Santa Claus told Shona McCullough that in the early 21st century, 526,403,012 children on Earth were expecting Christmas presents to be delivered by Christmas morning. (TV: Last Christmas)

The Fourth Doctor referred to child labour as one of the worst aspects of the Victorian era. (AUDIO: The Ghosts of Gralstead)

Some species were very compassionate towards children, such as the star whale. In fact, the last of this species willingly came to save the people of Britain because it could not bear to see their children cry and even continued carrying the population for their sake despite what had been done to it. (TV: The Beast Below) Another example was the mysterious Fairies, who not only refrained from harming children but required them to continue their race from time to time. (TV: Small Worlds)

A. Fergus and his crew ran like children when the Ninth Doctor, with blood on his face, told them to in early 2005 in Southbank, London. (PROSE: Have You Seen This Man?)

The 456
The 456 used human children as "the hit," presumably a type of recreational drug created by their bodily chemicals, which they said "felt good". They claimed that, once processed, these children lived forever. (TV: Children of Earth: Day Four)

In 1965, the 456 first arrived on Earth. They demanded twelve children, in exchange for a cure for a deadly new flu strain that would soon arise. Jack Harkness delivered the twelve children. The 456 left after releasing the cure, leaving behind Clement McDonald, which Gwen Cooper later speculated was because he was on the verge of puberty. (TV: Children of Earth: Day Three)

In 2009, the 456 somehow got every child on Earth to, at once, stop, and chant "We are coming." (TV: Children of Earth: Day One) The next day, the children chanted "We are coming - tomorrow." (TV: Children of Earth: Day Two) The next day, when the 456 returned to Earth, the children all pointed towards central London, where they had arrived, and chanted "We are here." (TV: Children of Earth: Day Three)

The 456 demanded that Earth hand over one tenth of the children of the world. Frobisher offered one child per million people on Earth. The 456 refused the offer; they demonstrated that by getting the children to chant a number: ten percent of all the children of the world. Jack, with Ianto Jones, interfered and demanded that no children be taken. As he demanded war, the 456 demonstrated their strength by poisoning and killing everyone in the building. (TV: Children of Earth: Day Four)

The next day, as per decisions made by the Cabinet of the United Kingdom, children were to be taken by bus to be "inoculated". In reality, they were being taken to be given to the 456. In the end, Jack defeated the 456 using the children to broadcast a signal fatal to the 456, but at a great cost: he had to kill his own grandson. (TV: Children of Earth: Day Five)

Davros considered the Daleks to be his children. (TV: The Stolen Earth, The Witch's Familiar, PROSE: Father of the Daleks)