The Sirens of Time were a species that fed insatiably upon the energy released by temporal distortions caused by changes in history. They could not change history themselves, only manipulate others into doing so. Those who answered the call of the Sirens twice were eternally enslaved to them.
One of the Sirens appeared three times in the Doctor's timeline. It first appeared to the Fifth Doctor as Helen, a crew member of a British merchant ship sunk by the U-20 in 1915, and manipulated him into preventing the sinking of the RMS Lusitania. This led to humans never going into space due to being devastated by disease due to someone from the ship killing the chemist Alexander Fleming. It next appeared to the Sixth Doctor as Ellie, a waitress on board the starship Edifice, and manipulated him into freeing the Temperon and the Knights of Velyshaa. It finally appeared to the Seventh Doctor as Elenya, the only survivor of a spacecraft crash, and manipulated him into saving Sancroff, who helped re-inspire the Knights of Velyshaa.
The result of these changes was that the Knights of Velyshaa were able to found a new empire, discover time travel and invade the planet Gallifrey. The Siren appeared to the three Doctors (who were brought to Gallifrey by the Temperon) as Knight Commander Lyena, who tried to manipulate them into un-doing the changes they had made to history. Doing so would have permanently enslaved them into creating more temporal distortions until the universe itself would have collapsed. The Doctors instead freed the Temperon, who sacrificed its freedom to contain the Sirens in eternal struggle. (AUDIO: The Sirens of Time)
The Sirens attempted to subvert the initial test flight of the first TARDIS. They used Punshon to change the cause of history. The TARDIS crashed. (AUDIO: Collision Course) They then caused havoc on the Dorset coast by opening up time holes which caused people to vanish into different eras. Kate Stewart and Petronella Osgood along with the Third Doctor and Jo Grant reversed their affect. (AUDIO: The Sacrifice of Jo Grant) Punshon was thrown out of the TARDIS and was split into two parts, one resided in the 1960s and the other in 1970s and caused the Rocket Men to be dragged back in time. The Seventh Doctor and Ace with the help of the Intrusion Counter-Measures Group managed to get the two parts of Pancham together to stop time collapsing. (AUDIO: The Split Infinitive) The TARDIS eventually became of planet which the Eighth Doctor, Bernice Summerfield and River Song discovered this but didn't know the cause of why the TARDIS had crashed. The Siren's made sure that the Doctor's companion Ria was killed in the process. (AUDIO: Lies in Ruins) The Siren's affect caused the changing and corruption of Earth's timeline which The Nine wanted to take. (AUDIO: Relative Time) The Sixth Doctor and Charley Pollard investigated these time distortions in the 18th century and 21st century and saw that the Siren's were the cause of it. (AUDIO: The Avenues of Possibility) The time distortions got the the point that it alerted the Time Lords and Lord President Romana II and Leela realised that they both had memories of visiting the planet Henlen when they travelled with the Fourth Doctor. Travelling to the moment which the Siren's changed history, Romana and Leela made sure that the test flight went ahead and succeeded with the help of the First to Eighth and Tenth incarnations of the Doctor. (AUDIO: Collision Course)