The Somnivores are an alien race who, as their name would imply, feed on "somnatic" energy, also called dream energy. While there are many different lifeforms in the universe that are classified as somnivores, including some Earth animals and plants, the alien race referred to as the Somnivores are more aggressive, attempting on at least two occasions to colonize the Earth and turn its inhabitants into dream batteries.
History
The Somnivores were first encountered by the First Doctor along with companions Nardole, Turlough and Captain Jack Harkness, who had been abducted and placed into the Somnivores' dream engine. They managed to escape and prevent the Somnivores from placing humanity in the engine, effectively stopping the conquest and colonization of Earth. (Gallifrey One 2018 Live Show)
They were next encountered by a later incarnation of the Doctor who found them in the silent ward of hospital in 1918 Toronto, Canada were they were found to be responsible for the Sleeping Sickness. (Lethargica)
Behind the Scenes
The Somnivores were the first original alien to appear in any form of The Game of Rassilon, and are one of only two aliens (alongside the Weeping Angels) to appear in the live show and the podcast.
As the podcast alludes to the Doctor having had a previous encounter with the Somnivores in the past - and with Dan Peck mentioning the 2018 live show - they serve as a link between the pre-podcast live shows and the narrative of the podcast, potentially canonizing the live shows. As a result, this wiki holds the editorial position that the live shows are part of the canon of the show.