The Sack of King's Landing
Tywin Lannister arrived at the gates professing loyalty, was let in, and sacked the city. Aerys ordered his pyromancers to burn all half a million people in it rather than yield, and his own Kingsguard, Jaime Lannister, put a sword through his back ÔÇö earning a name he will carry for the rest of his life from people who never asked what the alternative was.
The fuller tale
Tywin Lannister had sat out the entire war. He had not answered the king's summons and he had not answered the rebels', and when the Trident was decided he brought twelve thousand men to the gates of King's Landing and announced that he had come to defend the city. Grand Maester Pycelle advised opening the gates. The gates were opened.
What followed was a sack, carried out on a city that had surrendered. It was not a soldier's frenzy. Men went to particular houses. Elia Martell, Princess of Dorne and Rhaegar's wife, was killed in her rooms; her daughter Rhaenys was dragged out from under a bed; her infant son was killed against a wall. The men who did it were named afterward and rewarded rather than hanged, and Dorne has been waiting ever since.
In the throne room, Aerys gave the order he had been preparing for years: burn them all. There were caches of wildfire under the Sept of Baelor, under the guild halls, under the streets, enough to take half a million people with him. His own sworn shield, Jaime Lannister of the Kingsguard, killed the pyromancer and then killed the king, and was sitting on the Iron Throne when Ned Stark walked in.
The name he kept
Jaime Lannister was seventeen. He had broken the most serious vow a man in Westeros can swear, and he had done it to stop a city being burned. He was called Kingslayer for the rest of his life by people who never once asked what the alternative had been, and he did not explain himself, because explaining it would have required being believed.
Ned Stark found him on the throne and drew a conclusion, and the two of them disliked each other for seventeen years on the strength of a room neither would discuss.
Elsewhere in the wiki
 See the world as it stood in 283 AC What became of it  if an ending is written, it is here. Spoilers.
The chronicle records no ending here ÔÇö or none the maesters have set down.