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Rose Marion Tyler was the first companion of the Ninth Doctor and continued to travel with him after his regeneration into the Tenth Doctor. They developed romantic feelings for each other, but was sealed off in a parallel universe after the events of Doomsday
Biography
At age 19, Rose Tyler was living with her mother Jackie, in Powell estate in south London. She was working at Henrik's department store on Regent street when the Nestene consciousness began to invade the invade the city. Rose saved the Doctor who was being held by two autons. After assisting the Doctor in defeating the Nestene consciousness she joined him in the TARDIS. Their first trip was to the year 5 billion to witness the destruction of the Earth due to the sun expanding.

The 9th Doctor and Rose aboard platform 1 in the year five billion.
After this Rose felt uncomfortable watching her home being destroyed so the Doctor took her back to London in 2005 where she bought them both chips. Their next adventure was to Cardiff, Christmas Eve 1869, although the Doctor had intended to bring her to Naples in 1890. It was here the Doctor and Rose encountered Charles Dickens, and the Gelt. The Gelt had escaped to Earth through a rift, and were reanimating human bodies. The Doctor next took Rose back to her own time, although he had intended for it to be 12 hours after they had left, he made a mistake and arrived one year later. During this time, Mickey, her on again off again boyfriend, had been suspected of murder. Just after their arrival, the Doctor and Rose witness an alien ship crashing into Big Ben. This later turns out to be part of a plot by the Slitheen to turn the earth into a fuel source. Once the Doctor and Rose, with help from Harriot Jones, defeated the Slitheen they continued on their travels. They next landed in Utah in 2012 where they encounter a Dalek. During this the Doctor and Rose meet a young man named Adam, whom Rose is very attracted to. He joins the Doctor and Rose in the TARDIS, but the Doctor soon returns him to his own time after he deems him "not TARDIS material".
During her this first year with the Doctor, Rose convinces him to take her back to her parents wedding, the day her father died, so that she could be with him as he died. Rose however intervened and created a paradox. The Doctor was angry at her for doing this but allowed her to continue traveling with him. The Doctor and Rose next met another time traveler, Captain Jack Harkness, in London during World War II. 
The Bad Wolf
Rose at first was quite attracted to Jack, which led to the Doctor competing with him for her affection. Jack joined the Doctor and Rose aboard the TARDIS for a short time until the TARDIS crew were kidnapped and placed aboard the game station. Rose was placed in a futuristic version of The Weakest Link with a robotic Ann Robinson, where to be evicted results in death. Rose escaped the game but was captured by the Dalek fleet. After the Doctor rescued her, he sent her back in time by in the TARDIS by herself, because he thought the situation unwinnable. Rose opened the TARDIS console and looked into the heart of the TARDIS, gaining god like powers and becoming the being known as "The Bad Wolf".
Using these abilities she turned the Daleks to dust and end the time war once and for all.She also resurrected Jack who had being killed by a Dalek, in the process accidentally making him immortal in the process. The Doctor then absorbed the energy from Rose, saving her life, but bringing him close to death and forcing him to regenerate.
She continued to travel with the newly regenerated Doctor. During which they encountered Queen Victoria and witnessed the birth of Torchwood. After returning to her own time on Mickey's behest, the Doctor and Rose meet Sarah Jane Smith, who traveled with the Doctor many years ago. While at first Rose and Sarah Jane argued over who was the better companion, they soon became friends. After this, Mickey joined Rose and the Doctor in the TARDIS. On Mickey's first journey in the TARDIS, they landed on a abandoned spaceship, after which the TARDIS. The TARDIS crew then traveled to an alternate reality that the Doctor dubbed 'Pete's World'.

Rose and her father in 'Petes World'
While there Rose met an alternate version of her father, and Mickey met an alternate version of his grandmother (both of whom had died many years previously in their reality). After defeating the Cyberman, Mickey decided to stay in the alternate reality after his counterpart died. Rose and the Doctor then continued their travels during which they met a group called LINDA, devoted to following the Doctor. When the Doctor and Rose returned to Earth for Rose to visit her mother, Jackie told them that their were ghosts all over the world appearing at regular intervals on a daily basis. The ghosts were projections of Cybermen from 'Pete's World' caused by Torchwood's experiments. Once the Cybermen had fully crossed realities, they went to war with the Daleks, the Doctor was able to stop the war but he trapped Rose in 'Pete's World' in the process, seemingly forever.

Rose returns
Approximately 2 years later, Rose began to periodically appear trying to contact the Doctor. Her warnings did not get through to the Doctor, and the Earth was moved by Davros and the reformed Dalek empire to another part of space, to be used as a power source to destroy the universe. When the Doctor and Rose were finally reunited, the Doctor was shot by a Dalek.
This caused the Doctor to partially regenerate, resulting Donna Noble becoming part time lord, and a half human Doctor being created as well. Once the three Doctors had defeated the Daleks, Rose and the half human duplicate of the Doctor returned to 'Pete's World'.
Major Story Arcs
The Bad Wolf
During Rose's first season with the Doctor, the words Bad Wolf seemed to follow her and the Doctor everywhere they went. This was later revealed to have been created by Rose after she looked into the heart of the TARDIS and gained god like powers. She then referred to herself as the Bad Wolf and claimed that she had actually planted those words throughout time to lead herself to where she is now. She ceased to be the Bad Wolf when the Doctor absorbed the energy from her, saving her life in the process. During the events of 'Turn Left' she gave Donna Noble the message "Bad Wolf" to inform the Doctor that the walls between universes are collapsing.
The Torchwood Institute

Torchwood invaded by Cybermen
The Doctor and Rose land in Scotland 1879 where they meet Queen Victoria.
After an attempt is made on her life by an alien, she founded the Torchwood Institute to protect Great Britain from otherworldly threats and to capture the Doctor.
In 2007 the Torchwood mandate was the capture aliens and to study their technology with the unofficial slogan "If it's alien, it's ours". The word Torchwood was used by many characters in the second series until the season finale where the Doctor and Rose discovered the Torchwood institute, though it was destroyed and almost all the staff killed as a result of the battle between the Daleks and Cybermen. This story arc was continued in the spin off series Torchwood, featuring Jack Harkness as the main character.
The Stars Are Going Out

The Medusa Cascade
After Rose had been trapped in 'Pete's World', it initally seemed that she could never return. The Daleks however where planning to destroy the universe, a plan which had already being carried out in 'Pete's World' as it's timeline runs ahead of the regular universe. Due to this, Rose was able to return to the Doctor, along with Mickey, Jackie and her father. At the end of this story arc she returned to 'Pete's World' along with her parents, the half human duplicate of the Doctor, seemingly with no way of ever returning.