What is the Bay'ah? And has it been applied throughout Islamic history?

Bay'ah is the selection by the people of authority (Ahl al-Hall wal-'Aqd) of a man to lead the Ummah, to bring benefits and ward off harms. The chosen leader must possess ten qualities: he must be male, free, adult, sane, Muslim, just, courageous, Qurayshi, knowledgeable, and capable of leading the Ummah. If the Bay'ah is concluded with these specifications, then obedience to him becomes obligatory upon the Ummah, except in disobedience to Allah. The Bay'ah is concluded by the people of authority, and this was practiced after the death of the Messenger of Allah, peace be upon him. It is obligatory to fulfill the Bay'ah, even if the leader is immoral, in order to prevent discord.