Lord Grover Tully spoke for Prince Viserys Targaryen over Laenor Velaryon as the successor to Jaehaerys I in the GreatCouncil of 101 AC. When the Dance of the Dragons erupted in 129 AC, the oldlord proved loyal to his principles and King Aegon II … but he was aged then, and bedridden, and his grandson Ser Elmo defied him and had the gates barred and the banners kept close.
Later during the Dance, Ser Elmo Tully led the riverlords into battle at Second Tumbleton, but on the side of Queen Rhaenyra rather than King Aegon II, whom his grandsire had favored. The battle proved a victory—at least in part—and soon after his grandfather finally died and Ser Elmo became Lord of Riverrun. But he did not long enjoy his station; he died on the march forty-nine days later, leaving his young son, Ser Kermit, to succeed him.
Lord Kermit brought the Tullys to the height of their power. Vital and bold, he fought tirelessly for Queen Rhaenyra, and her son, Prince Aegon, later King Aegon III. Lord Kermit was the chief commander of the host that descended on King’s Landing in the last days of the war, and he personally slew Lord Borros Baratheon in the final battle of the Dance of the Dragons.
His successors ruled as best they could after him, but Riverrun was never again as prominent as during those years.
The World of Ice and Fire
Maybe it's just me, but do you ever find that the Tullys are kind of overrated? They don't seem to be on the same "level" as the other great houses. Even the Greyjoys, who appear to be much less respected, make for it based on sheer personality. The Tullys are just so. . .bland.