In the Game of Thrones series finale, it's revealed that Tyrion Lannister wasn't mentioned in the Archmaester's A Song of Ice and Fire book - but why not? As Tyrion says at the gathering in which Bran the Broken is elected the new King of Westeros, everyone loves a good story; there's nothing more powerful than a story that can be diffused as quickly as it's consumed. And so, based on Tyrion's speech, everyone present at the summit elected Bran as their new ruler.
But while Bran the Broken has a wonderful story to tell - a crippled boy who traveled north of the Wall and became the Three-Eyed Raven, and then eventually king - Tyrion has a particularly interesting story as well. Of course, Tyrion was initially known for being born a dwarf, but then he became Hand to King Joffrey, defended King's Landing at the Battle of the Blackwater, found guilty for Joffrey's murder, killed Tywin Lannister, fled Westeros and became Hand to Queen Daenerys Targaryen, and then came back to King's Landing to usher in a new age. But apparently, he's not worthy of mention in the history books.
Towards the end of Game of Thrones' series finale, Samwell Tarly presents Bran's small council with Archmaester Ebrose's new book, titled A Song of Ice and Fire (a meta reference to George R.R. Martin's own novel series upon which HBO's Game of Thrones is based on). But one thing stood out: Tyrion wasn't mentioned in the book. It's a callback to Varys' comment to Tyrion after the Battle of the Blackwater, in season 2, episode 10, "Valar Morghulis." Here's what Varys tells Tyrion:
"There are many who know that without you this city faced certain defeat. The King won't give you any honors, the histories won't mention you, but we will not forget."
As evident by his many accomplishments and involvements in Westerosi wars and politics, Tyrion has been integral to the Game of Thrones story, but people want to read about kings and queens, lords and ladies, battles and wars... not about a dwarf who became the hand of a king and queen. That's why the Archmaester doesn't put him in the book, but he was seemingly unimportant from an outside perspective, but very much indispensable in the grand scheme of things.
What's more, one of the last conversations that Tyrion has with Varys comes towards the end of "The Last of the Starks" when they were discussing treason against Daenerys. As Varys told him, "Have you considered the best ruler might be someone who doesn't want to rule?" It's what Tyrion refers to when he asks Bran to be king. Tyrion looks back to in his weeks of imprisonment when he came to the conclusion that Bran would be the best person to rule, not just because he knows their history but also because he's not interested in ruling.