As for his companion? They meet during an invasion of the Citadel. Everyone is fleeing in panic except for a young Quarian techie sitting in the Presidium dismantling a Cyberman, oblivious to the danger around her (“Run!”). After they save the day, she goes on the ultimate Pilgrimage, across all time and space. She’s a compulsive tinkerer and occasionally tries to reverse engineer and/or “upgrade” the TARDIS. She’s easily distracted by local technologies, cultures, etc, and as a result, never, ever stays put when told. She sometimes has terribly clever ideas and speaks in bursts of technobabble, which infuriates the Doctor (for an elcor value of “infuriate” anyway) because that’s HIS thing. After much hardship she gets to return to the Fleet, having taken the surname “vas TARDIS.”
Clara Oswald theory: Bad Wolf/Rose Tyler and Clara are somehow related
Bad Wolf was able to see all of time and space and mold it. (ep: Journey’s End)
Constant presence of roses around all three “versions” of Clara.
‘The most important leaf in human history’ was from a Norway Maple. (ep: The Rings of Akhaten). Darlig Ulv Stranden (a.k.a. Bad Wolf Bay) is located in Norway (ep: Doomsday / Journey’s End)
On 5 March 2005, Rose Tyler first met the Doctor. (ep: Rose) 5 March 2005 is also the date when Clara’s mother died. (ep: The Rings of Akhaten).
Clara is always wearing red clothes (or something red, like her bag in The Rings of Akhaten). Red is the color of most common roses.
The TARDIS doesn’t seem to like Clara (ep: The Rings of Akhaten). This may be due to the fact that she is an anomaly of the Universe. The same thing happened with Jack Harkness, since Bad Wolf gave him immortality. The TARDIS tried to shake Jack off (ep: Utopia).