The Big Four refers to the four contemporary leading Grand Ayatollahs of Twelver Shia Islam based in the holy city of Najaf in Iraq.
[1][2][3] All orthodox Twelver Shia Muslims follow the Islamic rulings of a Grand Ayatollah.
Under Saddam Hussein, the clerics were oppressed.
At present, the most prominent among them is Ali al-Sistani; who also serves as the head of the Najaf Seminary.
[4]