The Old Republic
The Jedi High Council was established approximately 4,700 BBY, created to provide a hierarchy within the forces of the Jedi Order and to advisory body to the Office of the Supreme Chancellor. Traditionally the Council is made up of twelve members, five lifetime members, four long-term members and three short-term members. The High Council members meet in the High Council Chamber with their headquarters in the Jedi Temple on Coruscant. They also met in the Chamber of Conclave which is a communication relay to all Jedi outpost, this would normally only be contacted annually by each outpost, however in times of war this has changed.
3,985 BBY the Mandalorian Wars breaks out and during which the High Council was still situated on Coruscant, but established several satellite councils to keep abridge of the current situation. However this created tension with several of the satellite councils, who upon seeing the pain and bloodshed requested the High Council for the permission to help, but were repeatedly denied. During the Mandalorian Wars the High Council not only had to deal with increasing numbers of Jedi who wanted to join the Republic forces, but with an internal Sith uprising. This Sith uprising started on the planet Taris and it intended to plant several member in and near the High Council and then assassinate them, replacing them with Sith. This was quickly quashed by the High Council, leaving the Republic and the High Council to cover the attack up as a Mandalorian terrorist attack.
After the Sith uprising had been dealt with the High Council had to be focus of the Jedi who had left the Order, Revan and his followers the Revanchist. They were condemned until the Council witnessed a vision of destruction of the people of Cathar. Revan and his followers were given command of the Republic force and ordered to drive the Mandalorian armies away from Republic space. Revan did such a good job that it scared the Council, so only Revan returned to face their wraith.
Revan demanded to take his forces and hunt down the remaining Mandalorians, the Council refused so Revan and his friend Malak left with a large portion of the Republic forces and left for the rim. They returned tainted and corrupted by the experiences, they started a new war Jedi Civil War for control of the galaxy in 3,959 BBY. Revan would later lose his memory and then redeem himself in the eyes of the Order, by driving away the Sith in 3,955 BBY.
In 32 BBY the Blockade of Naboo by the Trade Federation starts and the Council send out two Jedi, Qui-Gon Jinn and Obi-Wan Kenobi which start the off the events in the films.
During the blockade on Naboo, when the Sith Lord Darth Maul surfaced, the Jedi High Council consisted of Yoda, Mace Windu, Ki-Adi-Mundi, Kit Fisto, Plo Koon, Saesee Tinn, Depa Billaba, Eeth Koth, Even Piell, Yaddle, Oppo Rancisis, Yarael Poof, and Adi Gallia.
During the Clone Wars the Jedi order was in turmoil due to nearly all the masters being called out on active duty as generals in the war. And following the Great Purge, the Jedi Order was non-existent as all its members had died save Yoda. Shortly afterwards Yoda too died, meaning that there were no more Jedi Masters.
New Jedi Order
Fortunately Luke Skywalker using the teachings of Yoda, Obi-Wan and various holocrons of previous masters, trained himself to the level of a Jedi Master, and rebuilt the Jedi Order with himself as Grand Master. Many years later, Luke would restore the Jedi Council, and it's members would include: