Twins seem to run in the Lannister family, and none perhaps so famous as Jaime and Cersei. As the older son of Tywin Lannister and his cousin-wife, Joanna, Jaime is intended as the heir to Casterly Rock, but King Aerys II forces him into the Kingsguard instead. It's Jaime who kills Aerys during Robert's Rebellion, after the Mad King ordered him to kill his family and burn all of King's Landing with a wildfire cache. Aerys's vicious final orders are unknown to the public, who only know Jaime as the "Kingslayer."
Jaime spends many years in an incestuous relationship with his twin sister, Cersei, resulting in the birth of three children who are officially believed to be Robert Baratheon's. When Bran Stark catches them, Jaime shoves the boy out of a high window, nearly killing him. Jaime goes on a long journey during the subsequent war, eventually being captured by the Starks and sent back to King's Landing in exchange for the release of the Stark children held there. Along the way, his prickly animosity with Brienne of Tarth becomes something like friendship, although he does lose his sword hand to enemies.
After being reunited with his family, Jaime is given a prosthetic hand and a new sword. Over time, he becomes disillusioned with them, especially after watching his children die. He pushes for an alliance with other Houses to fight the White Walkers and, when Cersei double-crosses them, chooses to lead his own army North to help fight. He survives the battle and briefly starts a relationship with Brienne but ultimately returns to King's Landing, where he's killed alongside Cersei when the Red Keep is destroyed.