The season 6 of Game of Thrones is perhaps the first season for which D&D have very little source material as George R.R Martin expressed his disappointment when he couldn’t finish “Winds of Winter” on time, as a result show-makers had to depend on their own imagination and some of the previous material for season 6. For instance, Jaime Lannister going back to the Riverlands is part of Book 4 “A Feast for Crows” storyline where Cersei dispatches him to re-establish control of the Lannisters. Due to the inadequacy of new material, we have seen a lot more Bran visions and flashback scenes, for instance, Tower of Joy sequence. But I think it’s important as Bran Stark is the key to Iron Throne and battle against the White Walkers as he has world-changing powers.
We saw the Brienne telling her story to Podrick that men used to call her Brienne the Beauty, her father tried to marry her off thrice like a traditional lady of a noble house, but every time her engagement was called off. She was bullied and ridiculed by young noblemen. Finally, Lord Renly Baratheon accepted her and she became part of his Kingsguard.
In the past, George R.R Martin dropped a hint for a possible twist in the Winds of Winter, he said that it has to do with a particular character who is dead on the show but alive in the books. A few days ago, he was at a convention and he read passages from new material and revealed some interesting things about Brienne’s backstory. He named her the descendant of Ser Duncan the Tall, which is one of the most amazing lineages the character could have. He has often pointed to “Dunc and Egg” as the leading choice for the possible spin-off of Game of Thrones main series, should the HBO choose to do it.