The Rani, also known as Ushas, is a Time Lady, first introduced in The Mark of the Rani. Played by Kate O'Mara, she is the third 'major' renegade to be introduced to the series, the other two being the Doctor and the Master.
The Rani is a renegade Time Lady and scientific genius, who excels in genetic manipulation. She treats everything, including morality, as secondary to her own research and doesn't care how much suffering she must cause to get results.
She was expelled from Gallifrey after her laboratory rats - after numerous experiments - grew to a gigantic size and ate the Lord President's cat, as well as part of him. Prior to her exile, she seemed to develop a relationship - of sorts - with both the Master and the Doctor, but these are never expanded upon.
She took over the planet Miasimia Goria and enslaved the population to get more subjects for her experiments, which eventually led to her going to Earth in the 19th century to take a certain fluid from the brains of humans - the fluid that enabled them to rest, a function she had accidentally removed from the natives of her planet. (The Mark of the Rani)
Later, she would invade the planet of Lakertya and begin to build a super-brain there, using the minds of geniuses from Earth history - including Einstein and Louis Pasteur - in an attempt to detonate an asteroid made of strange matter, which is why she attempted to make the brain produce Loyhargil, a substance that would turn it into a time manipulator capable of controlling time anywhere in the cosmos. However, the Doctor foiled her plans. He interfered with the brain, causing the rocket that was supposed to detontate the asteroid to miss. The Rani fled back to her TARDIS, but was aprehended by her 'assistants', the Tetraps. Their leader took her back to Tetrapyriarbus, where he forced her to work to overcome their "plasma needs".
After many years, the Rani managed to escape from Tetrapyriarbus in her TARDIS fleeing the planet to be free of the Tetraps' constant need for blood. It was during this time that she started to put together her menagerie, intending to collect every species in the universe - initally for peaceful means, but as time went by she decided to use them for a few more devious means, such as capturing yet more subjects for her experiments.
Before she could act on her ideas, the Time War started and she was called into action. Due to the wounds that the Tetraps had inflicted on her during her enforced imprisonment, she was sent into the medical camps to assist the wounded and dying Time Lords sent into the camp on an almost by-the-minute basis. She never saw the front-lines, but tended to Romana and Leela whenever they came in bruised, burnt and bleeding - especially when Leela lost her sight, after which the savage was forced to stay with her in the camps.
The Rani fled Gallifrey around the same time as Romana did, taking her TARDIS as far away from her homeworld as possible as to avoid the shockwaves when it finally 'died'. Free of all commitments, she started filling up her menagerie yet again... and she came across Ace stranded on a deserted planetoid with a non-functioning TARDIS. In a rare show of pity, she took the girl aboard and began experimenting on her, with the end result being the 'dark' Senshi Dragonfire, someone who would help her greatly in the coming battle against the Sailor Senshi.
She arrived on Earth to battle against these Senshi, but had very little success to begin with - the Senshi were tough to beat and not very willing to be captured and experimented upon. In time, however, the Rani knew she would capture at least one of them and alter them, perhaps even turn them against their own. It's a game the Rani rather began to enjoy.