The Drast were a species of invaders who would slowly take over a planet.
Unlike other species, the Drast took over planets by shaping the economy until it was effectively controlled by the Drast. The Drast were led by the great Drast, who would send out Speculation Initiatives to gain control of the planet. This process could take years or generations of management. (PROSE: The Story of Martha)
The Drast were more advanced than the humans of the late 20th century, capable of travelling through space. The Drast also used disguises that functioned like a perception filter, allowing them to go unnoticed by the Master. The disguise could disable the perception filter used by Martha Jones. The disguise was hooked into the power grid, meaning they could not turn off the power without revealing themselves. The Drast were also capable of producing the Relativistic Segue, but only by reverse-engineering it from the black hole converter. (PROSE: The Story of Martha)
When the Master took over the world during the Year That Never Was, the Drast realised they would be unable to fight back against him and could not escape in the regular way. Instead, they hid behind their disguise and used their connections to study the Master's new technology. They were able to gain access to a black hole converter, which they brought back to their base in Yokohama. Under controlled testing, they were able to develop the Relativistic Segue. They planned to use it to escape, but they were unable to calibrate it correctly. When they tried to send Griffin through as a test, he was able to fight back and steal a gun, forcing the Drast to shut down the Segue. With it, the power grid and the disguises were turned off, allowing the Master to learn of the Drast. He sent in the Toclafane to burn down Japan. (PROSE: The Story of Martha)