The Tullys never reigned as kings, though they held rich lands and the great castle at Riverrun, at the fork where the river Tumblestone meets the Red Fork of the Trident, for a thousand years.
During Aegon the Conqueror's Wars of Conquest, the riverlands belonged to Harren the Black, King of the Isles. Harren's grandfather, King Harwyn Hardhand, had taken the trident from Arrec the Storm King, whose ancestors had conquered all the way to the Neck three hundred years earlier, slaying the last of the old River Kings. A vain and bloody tyrant, Harren the Black was little loved by those he ruled, and many of the river lords deserted him to join Aegon's host.
First among them was Lord Edmyn Tully of Riverrun. When Harren and his sons perished in the burning of Harrenhal, Aegon rewarded House Tully by raising Lord Edmyn Tully to lord paramount of the Trident and requiring the other river lords to swear him fealty. The Tully sigil is a leaping trout, silver, on a rippling field of blue and red. The Tully words are Family, Duty, Honor.
The present Lord of Riverrun, Lord Hoster Tully, committed himself to Robert Baratheon's cause against the Targaryen King when he wed his daughters to Robert's two closest companions, Lord Eddard Stark of Winterfell, and Lord Jon Arryn of the Eyrie. It was in his domain, at the Trident, that Robert Baratheon slew Rhaegar Targaryen, first son of King Aerys and heir to the Iron Throne.