I especially like how they are working with the Jaime and Brienne storyline, which is prompting me to write about those two and why I find them so intriguing.
I think one of the most interesting twists in book three is Jaime going from straight up villain to a relate-able character. In the show the disconnect is not as sharp because Coster-Waldau did a brilliant job giving him layers ever since the beginning. But in the books you only see the world from inside Jaime's head starting in book three. Before that , he is the guy who for some inexplicable reason loves Cersei, throws children from towers and doesn't honor his kingsguard vows.
It's not really so much a redemption arc (though it is that too) that he is going through, but more that you learn how he tics and how much being the Kingslayer shaped him. Jaime did a good thing killing the mad king, but all the supposedly "noble" characters despise him for it. And so he leaves morality behind altogether and only lives for people he actually loves, be it himself, Tyrion or Cersei.
Usually everyone who is fairly quick to judge him for the murder of the mad king or for sleeping with Cersei turns out to be a bastard in some way or another. Brienne is the person who really changes that. Jaime has settled to not live up to higher standards, he has resigned to be a villain and is convinced that everyone who claims to be any better is a hypocrite, except Brienne isn't.
At first Jaime perceives that as stupidity but when he finds it to be actual ideals it's like finding what he once aspired to be, only to find that true nobility and semblance of nobility sometimes exclude each other. Something he has stopped believing in has popped up in a completely unlikely place. At the same time when all the superficial value of his life is taken away from him with his arm (his ability as a knight, his place in the kingsguard that frees him from his father's grasp), those old values get infused with new life, by someone who lives them against greater odds than even Jaime has ever faced.
And Brienne who is herself a truly noble person starts, also against all expectations to recognize him as a kindred spirit, someone who has ideals and is willing to go great lengths (even unreasonable ones) for the people he loves. That she sees that makes it reality again for Jaime.
And the truly cool thing is that Brienne is no Sansa, she is not sitting around docile and believing in her man or waiting for a noble knight, she is a true knight herself, which raises her above all the false knights he is surrounded by and above all the ladies who in the end don't know what they are talking about when push comes to shove. It's a profoundly cool constellation for both characters. This bonding of enemies via honor is a very old motive in stories about knights, but it always always excludes women. They can never be part of that club, their honor always rest firmly between their legs. And here Jaime and Brienne break this wall down. Instead of burning love, the only allowed feeling between men and women in the heteronormative movie world, there is genuine respect for each other.