John Who and Gillian Who (Beware the Trods!) were siblings. According to some accounts, they were the grandchildren of the Doctor and travelled with him during his first and second incarnations. (The Klepton Parasites to Invasion of the Quarks) According to other accounts, they never existed, but were either the dreams of the Doctor (The Land of Happy Endings) or the creations of the Master of the Land of Fiction. (Conundrum)
As real beings
Some accounts held that John and Gillian were real, corporeal beings. According to these, John and Gillian first met their grandfather in 1960s England. They knew he was some kind of inventor, but had evidently never seen him or travelled with him when they found the TARDIS in an empty yard. They entered and he acknowledged them as John and Gillian. During their visit, John playfully touched a button on the console and the TARDIS took them to the 30th century, where they helped the Thains defeat The invading Kleptons. (The Klepton Parasites)
John and Gillian travelled with the Doctor on many adventures, fighting enemies such as Captain Anastas Thrax (The Hijackers of Thrax), the Zarbi (On the Web Planet), the Gyros robots (The Gyros Injustice) the Pied Piper (Challenge of the Piper) and the Trods. (Beware the Trods!)
The Doctor parted company from them, but reunited with them in his second incarnation. From their perspective, little time had passed. They resumed their adventures and fought other enemies, including the Daleks and the Cybermen, until they reached their teen years, when the Doctor enrolled them in university on Zebadee to keep them safe from the Quarks. (Invasion of the Quarks)
John eventually became a professor and wrote a memo on the dangers of the Trods to Colonel Marc Forest of Special Space Security. At this time, John styled himself “Professor John Who”. (Beware the Trods!)
As imaginary beings
One account claimed that The “Dr. Who” who had travelled with his 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. (Conundrum)
Land of happy endings
The Eighth Doctor had dreams in which he had adventures with John and Gillian. These dreams helped the Time Lord unwind by suggesting a less complicated reality where “villains are naughty, not evil”, “people never die” and “promises are never broken”. After one such dream, the Doctor awoke refreshed and re-energised. (The Land of Happy Endings)
John could be known to be rather protective of Gillian, growing upset when she was accidentally left behind when he and the Doctor returned to the TARDIS. (The Ordeals of Demeter)
Behind the scenes
It does not appear that John and Gillian had met the Doctor before the comic story The Klepton Parasites, although they were aware of his existence and the Doctor’s comment upon their arrival implies that he was expecting them. Nothing was ever revealed about their lives before meeting him.
The characters of John and Gillian were created for the Doctor Who comic strip in lieu of using (and paying license fees for) any of the companions from the television series. From the start, Polystyle Publications’ rights to use Doctor Who in comic strip form allowed them to use only the title of the television series, the TARDIS and a likeness of William Hartnell.
At the conclusion of the comic story The Monsters from the Past, Gillian shoots the villain dead, making her one of the few sympathetic, recurring characters other than Leela, Romana I and UNIT personnel to be shown killing, prior to the BBC Wales era.
In the novella Time and Relative by Kim Newman, Susan Foreman has friends at Coal Hill School named John Brent and Gillian Roberts, named after John and Gillian from TV Comic.