The Dance ends, and the dragons end with it

Rhaenyra is destroyed by her half-brother in the cruellest way the war could arrange, and Aegon II outlives her by months before he is poisoned. The throne passes to a traumatised boy, Aegon III, who will be remembered as the Dragonbane: within twenty years the last of the dragons is a stunted, sickly thing that dies in the Red Keep, and the Targaryens are simply a family with silver hair.

The fuller tale

Rhaenyra fled the city she could not hold and went back to Dragonstone, where her half-brother was waiting with the last of Sunfyre. What he did to her there was not an execution. He fed her to the dragon in front of her surviving son, and had the boy watch, and it took a long time, and the maester who wrote it down could not make it a tragedy because it was only cruelty.

Aegon II outlived her by six months, ruined, in constant pain, unable to walk without help, presiding over a war he had already lost in the north. He was poisoned in his own hall by his own side, because the lords had finally decided that peace was worth more than either of them. Nobody was ever punished for it, which tells you how broad the agreement was.

The throne went to Aegon III ÔÇö Rhaenyra's son, ten years old, the boy who had been made to watch. He was married to Aegon II's daughter, so that the peace would be a marriage, and he reigned for twenty-six years and is remembered as the Dragonbane. He never flew again and never spoke of it, and it is said he could not be got to enter the Dragonpit ruins for any reason at all.

The end of the dragons

Of the twenty dragons alive when the Dance began, four were left when it ended, and none of them thrived. Attempts were made to hatch more; the eggs went to stone. Under Aegon III the last of them was a stunted, sickly thing the size of a dog that could not fly, and one morning in the Red Keep it was dead, and that was the end of it.

There has been argument ever since about whether the dragons died of the war, of inbreeding, of confinement, or of something the Citadel did quietly ÔÇö one Grand Maester's papers were burned in a hurry after his death, which has kept that theory alive for a century and a half. What is certain is that after 153 AC House Targaryen was a family with silver hair and a very uncomfortable chair, and every claim it made rested on a memory.

What it cost

The Dance killed more Targaryens than any other event in their three hundred years, wrecked the riverlands, emptied the treasury, and taught every lord in Westeros that the royal family could be fought. Every rebellion for the next two centuries is standing on this one.

Elsewhere in the wiki

 See the world as it stood in 131 AC 

What became of it ÔÇö if an ending is written, it is here. Spoilers.

The chronicle records no ending here ÔÇö or none the maesters have set down.