When the Ninth Doctor first met Rose Tyler, she was a very emotional nineteen-year-old living on a London council estate who left school with minimal educational achievements. Shaped by living with her promiscuous mother and stories about her father she never knew, Rose was destined for a life in retail. However, the Doctor blew up her store and the pair began travelling together afterwards. Rose helped the Doctor work through some of the pain he harbored from surviving the Last Great Time War. When she met the Doctor, Rose was the girlfriend of Mickey Smith, but their relationship began to decay after she started travelling in the TARDIS. As Mickey himself noted, she transferred her romantic attention to the Doctor.
A major facet of her time in the TARDIS was that she had caused a temporal paradox by which she was the reason she became the “Bad Wolf”. Leaving clues throughout history that she was able to recognise when all her hope had evaporated, that helped find her way back to the Doctor, even though he had abandoned her and the TARDIS. Unable to actually fly the time machine, she stared into its heart, which enfolded her in time vortex energy and turned her into a new and seemingly omnipotent being capable of rescuing the Doctor. The experience nearly killed her and forced the Doctor to absorb the time vortex energy and transfer it back to the TARDIS — a traumatic act that naturally triggers regeneration.
Rose was forced to stop travelling with the Tenth Doctor once she was pulled into a parallel universe. She spent years trying to find a way back to the Doctor and when she found one, the Doctor explained that she had to remain in her new universe with her mother, new baby brother, that universe’s Pete Tyler and, for a time, Mickey. Ultimately she got most of her wishes fulfilled when a duplicate Tenth Doctor came to live out the rest of her life with her.
Captain Jack Harkness
“Captain Jack Harkness” was the alias adopted by a Time Agent and con man from the 51st century who became an associate and occasional companion of the Doctor. After being exterminated by a Dalek, he was revived by Rose Tyler after she absorbed the Time Vortex. Unable to control her powers, Rose accidentally turned him into an immortal being. Because of this, the Ninth Doctor saw Jack as a fixed point — a temporal paradox that threatened the TARDIS’ proper operation. Consequently, the Doctor abandoned him in the year 200,100 aboard a space station orbiting a Dalek-devastated Earth. Stranded, Jack had to use his own devices to catch up to the Doctor. He thought it likely that he’d find the Ninth Doctor in the early 21st century, since that was Rose’s home era. But his vortex manipulator failed to deliver him there, leaving the immortal no choice but to simply wait from the mid-19th to the early 21st century to reconnect with the Doctor.
During his long wait for the Doctor, he experienced Earth’s history first hand. For the majority of those years, he also worked for Torchwood Three. For several decades an informal free-lancer, he eventually became its head in the year 2000. Later that decade, he finally met up with the Doctor, although the Time Lord had by this time regenerated into his tenth form and was now travelling with Martha Jones.