52nd century

By the 52nd century, the Earth no longer had winters, due to pollution. Environmentalists were concerned about the warp footprint of vessels. (PROSE: The Frozen) Major powers included a race of Cybermen that held power over a quadrant of the galaxy and several religious orders, such as the Church, which remained a large, powerful organisation since the previous century, and the Order of the Headless. Time-active factions such as the Justice Department and the religious order known as the Silence were also seen in this century, but it is not known if they were native.
The Doctor visited the Gamma Forests and saved a young Lorna Bucket. (TV: A Good Man Goes to War) The Eleventh Doctor got the Teselecta to help him cheat death in 2011. (TV: The Wedding of River Song)
Kovarian and the Church abducted Amy Pond and later her infant, intending to use the baby as a weapon against the Eleventh Doctor. The Doctor appeared to capture the base Demons Run from them, but this was a trick and the baby Melody Pond remained in their hands. In the process of finding Amy and Melody, part of the Twelfth Cyber Legion was destroyed. (TV: A Good Man Goes to War) Dorium was decapitated on Demons Run. (TV: A Good Man Goes to War) His head survived, and spent its days in the Seventh Transept. (TV: The Wedding of River Song) An adult River Song studied archaeology and was imprisoned at the Stormcage Containment Facility in this century. (TV: Let's Kill Hitler, The Pandorica Opens)
Human historians associated the Stormcage Containment Facilities with the 52nd century. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe) By the 53rd century, a Stormcage (perhaps one of many) had been renovated, and became known as the Hesguard Institute. (COMIC: Sin-Eaters)