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, (POEM: 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 one version of the Eighth Doctor who had recently encountered Spring-heeled Jack (COMIC: The Curious Tale of Spring-Heeled Jack) had dreams in which he had adventures with young versions of John and Gillian. The Doctor believed that he dreamed this world to envision a reality where "villains are naughty, not evil", "people never die", and "promises are never broken".

However, by one reading of this account, the world of John and Gillian potentially was real, as both Eighth Doctors dreamed of each other, meaning the "Spring-heeled Jack" reality could be the dream world or that both realities could be real independently. (COMIC: The Land of Happy Endings)

It's important to note that the above two sources were not consistent with John and Gillian eventually growing older and leaving for Zebadee University. (COMIC: Invasion of the Quarks, Beware the Trods!)

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. (POEM: The Five O'Clock Shadow)

Behind the scenes
One commonly repeated claim is that the authorial intent of The Land of Happy Endings was to retcon that all John and Gillian strips were nothing more than dreams in the Doctor's mind. The truth is more complex.

The original concept for the story was simply to bring back the pair to celebrate 40 years of Doctor Who comics. Writer Scott Gray initially conceived of a plot as featuring an elderly John Who reliving his adventures in a virtual reality after the death of Gillian. The Eighth Doctor would have entered the virtual world to confront him and save him. However, when he described this idea to Clayton Hickman, Hickman's reaction was that of nausea, so the idea was abandoned. (The Flood)

Eventually, presenting the world of TV Comics as one that the Doctor thinks fondly of and dreams of to escape was deemed a better fit. The story was meant to be metaphorical, as many adults dream of the simpler times in their youth. Scott Gray would later state:

"On the final page, you had the Paul McGann Doctor as he is now, waking up. And we realize that what he's been having is basically a really nice sweet dream about his grandchildren... And I didn't want to say, "it's just a dream. This is how they exist." I wanted to suggest that, "Yes, it's a dream. But it's also real. This is just one more reality." And that John and Gillian are every bit as much real as every single companion you've ever seen on TV, or in the comics or in the books..."

- Scott Gray