Celestis

The Celestis were the Celestial Intervention Agency after they removed themselves from history to escape the War.

Nature
The Celestis removed themselves from history and detached themselves from the physical plane of existence, making themselves ideas, and so harder to destroy (harder than a physical body tied down to the timeline).

They inhabited a world outside the normal space time called Mictlan, a place constructed using the Matrix. It existed outside the physical universe.

The Celestis were split on whom to support during the War: the Time Lords or the Enemy. The Celestis took those on the brink of death to Mictlan. (PROSE: Alien Bodies)

They believed themselves gods and aloof from the Spiral Politic. Due to the nature of their existence, they required people to act on their behalf as well as think of them to exist. To do this they often appeared to lesser beings in the form of gods. (PROSE: The Book of the War)

Interactions with history
The Sidhe were aware that the Celestis were collecting those that died during the Battle of the Bulge. (PROSE: Autumn Mist)

The Celestis established complete control over the government of a major country on early 21st century Earth. (PROSE: Head of State)

The Celestis made a deal with the early 21st century scientific genius Jimmy Moriarty which involved giving him knowledge of a ritualistic method of time travel. (PROSE: Erasing Sherlock)

Destruction
Because their human slaves were alive in the City of the Saved, the Celestis knew that Mictlan would one day be destroyed. (PROSE: The Book of the War) After the Eighth Doctor put a Celestis Mark of Indenture on the Shift, it was kept in a zoo in Mictlan and lived through the fall of the Celestis under the Memeovore. (PROSE: The Book of the War)

This came to pass when their former agent, One, arranged for the Memeovore to devour Mictlan and be subsequently cut away from the rest of the Universe by the Doctor and a fleet of War TARDISes, when he learned that Mictlan could attract the vast Swimmers to this universe. As a result, the Celestis were virtually all destroyed. (PROSE: The Taking of Planet 5)

Behind the scenes
Rassilon's plan for the Time Lords to survive the Ultimate Sanction at the end of the Last Great Time War by becoming "creatures of pure consciousness" resembles the actions taken by the CIA in becoming the Celestis. (TV: The End of Time)