The Vardans were a telepathic race with the ability to mentally travel along any broadcast wavelength. They were a militaristic race, living by the principle of "survival of the very fittest."
The Vardans contacted the Doctor to assist them in their plans to conquer Gallifrey. The Doctor pretended to help them, but placed their planet in a time loop. At the same time, Gallifrey was invaded by Sontarans, who were using the Vardans so that they could conquer Gallifrey themselves. (DW: The Invasion of Time)
The Vardans were ridiculed as the only race ever outwitted by the Sontarans.
Mortimus used Artemis to release Varda from the time loop and suggested that they invade Earth. This invasion was also defeated by the Doctor, who trapped them in a standing wave, then beamed them back to Varda. When the invaders arrived home 5000 years later, they found that a government revolution had occured during their absence and that their race had abandoned military conquest. (NA: No Future)