Utopia was a planet, believed to be one of the last remaining habitable worlds in the universe. The Utopia Project was named after it. The purpose of the project was to send the remaining survivors of humanity to the planet based on a modulating (non-automatic) signal beaming”Come to Utopia”. Legends spread about this world, such as that the skies were made of diamonds.
In the year 100,000,000,000,000, several thousand years after the foundation of the Project and not long before the anticipated end of the universe, the remnants of humanity took off from Silo 16 on Malcassairo to Utopia in a rocket. They hoped to live the rest of their lives there. (Utopia)
However, the planet they crashed on was cold, dark, and inhospitable. The humans barely survived by sealing themselves into spherical shells. They regressed to the Toclafane. As part of the Master’s scheme to take over the planet Earth in the 21st century, the Time Lord shuttled back and forth between that time period and Utopia (using a TARDIS stolen from the Tenth Doctor). He took his wife, Lucy Saxon, to the planet at one point.
The Toclafane, with The Master’s help, left Utopia before it went nova. They travelled through a time rift created by The Master to 21st century Earth. They took shelter and control of the planet for a year. Ultimately, however, the efforts of the Doctor, Martha Jones and Jack Harkness resulted in not only the Toclafane invasion being defeated, but time itself rewinding, creating the Year That Never Was. Consequently, the Toclafane never left Utopia, and shortly afterward the planet was destroyed by heat death. (Last of the Time Lords)