Reclusive Time Lords, watching over all of time and space, what's their game? Gallifrey
By: +David Herron; Date: April 22, 2017
The War Games
The War Games was a very long story arc where eventually some curious time traveling aliens were found to have created an arena, for unclear purposes, of fighting battles. The whole scenario was too much for The Doctor to handle, and he appealed for help from Gallifrey, under great duress. After helping to resolve the situation, the Time Lords subjected The Doctor to an enquiry after which they determined to exile him to Earth for awhile.
The Deadly Assassin
In the middle of the 4th Doctor's time, he was summoned to Gallifrey. While there he was framed for murder, but was able to turn the tables and ....
You'll notice their garb has changed, and now they're wearing this weirdo head-dress thingymajob.
Outside the City are people who live in the wilderness. The theme being soft city dwellers in an artificial cocoon, versus outsiders living in the real world.
The Five Doctors
During the 5th Doctor's time, they brought five of his incarnations together for a foray into a forbidden zone on Gallifrey. It was described as terrain in which Time Lords would sometimes have deadly contests. In the center of the zone was a "fortress" of sorts guarding the Tomb of Rassilon, an especially powerful Time Lord who was imprisoned in the forbidden zone. However, Rassilon had entrapped a few Time Lords in his tomb.
The End of Time
Rassilon somehow eventually freed himself from his imprisonment. In The End of Time we see him as the Lord President of Gallifrey, ruling with an iron fist that can vaporize Time Lords.
Apparently it was Rassilon's supreme power-thirst which caused the Time War? It was the Time War which pitted Gallifrey versus the Daleks in an ultimate battle for supremacy, and in which apparently hugely grevious monstrosities were born.
The Day of the Doctor
This is The War Doctor returning to his home turf. It's been shown that The Doctor used this barn as his childhood sleeping quarters. When the War Doctor resolved to end it all by unleashing an ultimate weapon, he returned to this place.
He had sized The Moment, a.k.a. this "ultimate weapon" which also incorporated in itself great wisdom with which to enquire as to the potential use of The Moment.
After the death of Clara Oswald, the Doctor resolved to save her. He made his way to Gallifrey, after which he forced the Time Lords to retrieve Clara from time stream, in a way that she skirted around death. After that they stole a TARDIS and flew off into the sunset. Well, to the very end of the universe.