The Toclafane invasion would have occurred in the early 21st century on Earth, but, due to the actions of the Tenth Doctor, Martha Jones and Jack Harkness, the invasion never took place and only a few actually remembered it happening. (TV: Last of the Time Lords)
The origins of the Toclafane Invasion lay in the last of humanity at the end of the universe in the year 100,000,000,000,000 trying to find a way to survive. They eventually tried to reach Utopia. With Martha, the Tenth Doctor and Jack's help, the scientists Yana and Chantho were able to activate the rocket to send the humans to Utopia.
The last of humanity boarded the ship and were sent away. (TV: Utopia) They soon realised there were no "diamonds" and cannibalised their bodies into the Toclafane, becoming childlike in order to survive, though it didn't work since the universe was still collapsing around them. Sometime later the Master would return to offer them a chance to return to the universe and start again. (TV: Last of the Time Lords)
The election and invasion Edit
With the help of a paradox machine, The Master brought the Toclafane to Earth in the 21st century. He ordered them to kill President Arthur Winters, along with a tenth of the Toclafane's human ancestors. (TV: The Sound of Drums)
The year that never was Edit
One year later, the Master planned to launch the entire Toclafane fleet towards the universe itself, as he had plans to rule the entire universe and create a New Time Lord Empire. Martha travelled to London to stop him, but she was caught by the Master and taken aboard the Valiant, who had been aware of her presence. In fact, she had tricked Professor Alison Docherty into revealing her location while she told a story that would make all of humanity say "Doctor" at one moment in time. The Doctor spent the year psychically tuning himself into the Archangel Network of satellites, and his youth was restored. Jack Harkness destroyed the paradox machine. The Toclafane vanished from the skies of Earth and were teleported back to Utopia and thus they never invaded. Time reversed by one year and everyone forgot except for those aboard the Valiant. The only remaining impact of their invasion was the death of the president and the mental instability it inflicted on the Jones family. (TV: Last of the Time Lords)
While the invasion proper never occurred, the incident concerning the murder of President Arthur Winters at the hands of the Toclafane was reported as an invasion by Trinity Wells. (AUDIO: Driving Miss Wells) Subsequently, Harold Saxon completely disappeared from the perspective of the general public. (TV: The End of Time)