Aenar relocated his family to Dragonstone after his daughter, Daenys, had a prophetic dream that foretold of Valyria's destruction. He brought five dragons with him, one of them being Balerion. Because of this, Aenar was stripped of his ancestral home and titles, and known as a coward within Valyria.
After the Doom, House Targaryen became one of the last few houses of Valyria, along with Houses Velaryon and Celtigar. The Targaryens were the only ones who owned dragons. Aenar was eventually succeeded by his son, Gaemon.