John and Gillian's world

"John and Gillian's world" was the setting of Dr. Who's adventures with his grandchildren John and Gillian. (COMIC: The Land of Happy Endings)

Accounts differed as to whether these adventures took place in reality (PROSE: Beware the Trods!, The Man Who (Nearly) Killed Christmas) and John and Gillian were truly the Doctor's grandchildren (COMIC: The Klepton Parasites, et al.) or simulacra, (PROSE: The Five O'Clock Shadow) or if they took place in the Land of Fiction (PROSE: Conundrum) or the Doctor's dreams. (COMIC: The Land of Happy Endings)

History
to be added

Nature
One account suggested that the "Dr. Who" who travelled with his two grandchildren existed in the Land of Fiction. While visiting, the Seventh Doctor encountered a "John" and "Gillian" who claimed he was their grandfather in whose company they had fought the Kleptons and the Trods. They tried to make him remember that his name was Dr. Who, to which he flatly replied with denial. When they pressed further and asked if he remembered them, he said that he didn't. (PROSE: Conundrum)

Another, unrelated account stated that the Eighth Doctor had dreams in which he had adventures with a version of John and Gillian. These dreams helped the Doctor unwind by suggesting a less complicated reality where "villains are naughty, not evil", "people never die", and "promises are never broken". However, despite the second claim, the Doctor, in the dream, was seen to intentionally destroy a number of apparently sentient robots. After one such dream, the Doctor awoke. (COMIC: The Land of Happy Endings)

In yet another account, John and Gillian did indeed physically exist and travel with the Doctor, but they were mathematically-computed simulacra given reality by the TARDIS based on the Doctor's wishes. They were only two of "thousands" of companions whom the Doctor had created out of thin air, perfect and unchanging, to travel at his side without fear of death, in an effort to avoid responsibilities and anxiety. These evading techniques led to the creation of a psychic entity known as the Five O'Clock Shadow, which the Doctor ultimately escaped by using the same TARDIS functionality to give life to perfectly angst-free versions of himself and Susan. (PROSE: The Five O'Clock Shadow)