The Breaking of the World and the Long Night that came after it were the events that ended the Age of Legends. Destruction of all the knowledge, change of the shape of the world and madness of male channelers is very well documented and proven. We do not know all, but we know much: the truth about Lews Therin's descent into madness and the Dark One's counterstroke among them.
But there is an event that is also known to have happened, although we know almost nothing about it. The Long Night was a terrible darkness that fell upon the entire world soon after the last male channeler was Gentled. An unnaturaly long and cold winter started, lasting for an entire generation. All the cultures of the world remember it and every tongue on earth has one name for it.
No one knows how exactly it started. The Rhoynar believe that the Mother River froze because of the hearts of men, and that it was free only after all the Rhoynar sang the music that brought back the light. On the islands in the Aryth Ocean, like those of Old Valyria, people say that the sun rebelled against the Creator and refused to show it's face until a woman with a monkey's tail convinced it otherwise. Dothraki believe Komu, their horse god, died and light died with him, until he returned from the dead back into glory of immortal life.
Another story, of particular interest, is that of the hero named Azor Ahai. According to the tale, Azor Ahai struggled to stop the Long Night, working endlessly in his forge. At last, after his previous weapons all failed, he worked on a legendary sword, Lightbringer, for hundred days and hundred nights. He at last called his wife Nissa Nissa and, with a heavy heart, plunged the Lightbringer into her heart. The fire of her hurt burned and enveloped the sword. Thus, the light was brought back to the world.
(This story is of particular interest because it bears striking similarities to the history Lews Therin. The Champion of the Light is thus believed to be a source of this legend.)
But the most complete version of this story is in the Westerosi legends. According to those stories, the White Walkers came from the far North. Creatures of snow, clad in ice and crowned with cold, they were the offspring of the Great Other, and they brought cold and death wherever they went, riding their dead horses and hunting with their packs of pale spiders, as big as hounds. They led their armies of corpses, making all life, light and warmth flee from them. Then, the Last Hero emerged, and, after many adventures, in which all of his companions died, he reached the Children of the Forest. He founded the last alliance of Giants, Humans and the Children, gathering everything they could. Together, they managed to drive back the Others back to the North. And so, the Wall was built and the Night's Watch was founded.
This is the only version that has concrite evidence in today's world: the Wall exists, and so does the Night's Watch. Children of the Forest and Giants, though long gone, were real.
Both the maesters of the Citadel and the Brown Ajah sisters of the White Tower have struggled for centuries to find some explanation for these events outside of the theory that states the White Walkers brought the Long Night. The Aes Sedai allowed the more supernatural interpertation, some positing that it is possible it was the side effect of saidin beng tainted. The maesters, however, always skeptical of magic, even when meeting with the Aes Sedai, always sought more rational explanation.
The Brown Ajah, however, have always found one passage in the Karaethon Cycle of particular interest:
"Night gathers and snow comes with it,
the sun shall be gone and dead,
the Great Deceiver shall stretch out his hand,
and call his slaves from the winterland.
No one will see, no one will hear,
for all will care for gold and throne,
winged snakes shall roam the sky,
and in that darkness the dead will rise.
Yet then will come he who was born before,
he will break the chains of slaves,
he will send the Other away,
he will bring death to the dead.
His kind will hate him because he brought them war,
but the Slaves shall love him and remember him,
for he broke their chains and saved them from the Great Other."
(Written by Ardell, maester of the Citadel, one of the few who travelled east to the Land of Artur Hawkwing).