House of the Dragon is currently covering the events in Targaryen history known as the Dance of the Dragons. This is a particularly bloody and chaotic period of Westerosi history, but there are several other notable events that occurred even before this. The series is currently in the year of 129 AC in the Westerosi calendar, which begins from the date Aegon the Conqueror was crowned in Oldtown and officially became King of the Seven Kingdoms (though the Targaryens would not claim dominion over Dorne until after House of the Dragon takes place, they still claimed the title - a bit of wishful thinking).
The histories of Westeros supposedly date back thousands of years (though this figure is likely exaggerated), but House Targaryen itself only became notable about 112 years prior to Aegon's conquest. Prior to this time, they were a dragon riding family of old Valyria, but not one of the most powerful. There were about forty such families in total, and the Targaryens ranked somewhere around the bottom of the ladder.
The Doom of Valyria
It was the Doom of Valyria that first set the Targaryens apart. One of their own members, Daenys the Dreamer, was a prophet. She had 'dragon dreams' filled with portents of the future. One dream warned her of the coming cataclysm that would destroy Valyria. She warned her father, who believed her, sold all of House Targaryen's Valyrian holdings, and took the family and their five dragons to settle on Dragonstone to the east of Westeros. The other Valyrians mocked him, and he became known as Aenar the Exile thereafter.
The Targaryens would be spared from the Doom of Valyria when it occurred twelve years later, and ended up being the last family in the world that had dragons at their disposal. In a single day, the fourteen super volcanoes composing the Valyrian peninsula exploded and completely eradicated the empire. Some other Dragonlords survived, but they were killed while trying to re-establish Valyria. The Targaryens kept to themselves, mostly, for the next century, while chaos reigned. The Dothraki emerged as the dominant power where Valyria once held sway, the Free Cities became independent, and Valyria was said to be cursed forevermore.
The Conquest of Westeros (And the Dornish Resistance)
The Targaryens were mostly a curiosity to the Westerosi for the century that they remained on Dragonstone. While the Targaryens were isolated, the Seven Kingdoms warred. One King, Argilac the Arrogant (ancestor of the Baratheons) was on the verge of losing his kingdom entirely to the Ironborn. He reached out to Aegon the Conqueror and offered him certain contested lands and the hand of his daughter. Aegon was already married to his two sisters, Visenya (rider of Vhagar) and Rhaenys (rider of Meraxes), however, and took it as an insult that Argilac would offer contested lands as a dowry. For reasons not entirely known, Aegon then decided to wage war on the continent and conquer it in his own name. He set about doing so, wiping out entire Houses and taking six of the Seven Kingdoms in just two years.
The Dornish were experts at guerilla warfare, however, and eluded conquest. Despite years of war, they refused to capitulate. Tragedy struck Aegon when the Dornish scored a lucky shot on Rhaenys' dragon. Her body was never found. Aegon and his sister Visenya waged a war of retribution on the Dornish, raining fire and blood down on them. This ended, however, due to a very mysterious letter. Prince Nymor of Dorne sent his daughter Deria to treat with Aegon, and she gave him a letter to read. The contents of it are unknown, but Aegon is said to have cut himself on the Iron Throne when he read it, and fled to Dragonstone for the night. On his return, he agreed to peace.
Maegor Targaryen Rules for Six Years, Six Months, and Six Days
Aegon the Conqueror had two sons: from Rhaenys, he had his son Aenys, his heir. From his sister Visenya, he had Maegor. Aenys would rule for some years after his father's death, but he proved to be weak and ineffectual. Eventually, he died at a young age (his aunt Visenya was rumored to have a hand in that). Maegor usurped the Iron Throne, which was set to go to Aenys' son Aegon. Maegor claimed Balerion, the largest Targaryen dragon, and killed Aegon on his dragon Quicksilver in short order. He inspired the anger of the Faith of the Seven, who had warriors in those days, when he took another wife (his first had not given him any heirs, none of his wives ever would). Eventually, the conflict boiled over, and Maegor faced a trial by combat against seven champions of the faith and six of his own companions. He took a terrible blow to the head.
He lingered between life and death for a month. Some say he did die, and a sorceress named Tyanna (who would become another of his wives) brought him back to life, similar to what happened to Jon Snow. When Maegor woke from his coma, he was more vicious and cruel than he had been before. He immediately set to killing as many members of the Faith as he could, forcibly wed his niece Rhaena (widow of Aegon), and was prone to mercurial fits of rage. His end came when his nephew, Jaehaerys (last son of Aenys, who would soon succeed Maegor) began to march on King's Landing. Maegor was found impaled on the Iron Throne, though the throne room had been locked from the inside, and none had been seen entering it.
Silverwing Refuses to Go North
Many years after Maegor's demise, Jaehaerys had married his sister, Alysanne. A curious episode happened when Alysanne engaged in a royal progress to the North. While visiting the Wall, she desired to take her dragon, Silverwing, north of it. The dragon had never defied her, but the queen could not make the dragon go past the Wall. She wrote that it was as though there was an invisible barrier blocking the path, or that there was something the dragon did not want to face. It seemed to be an ominous portent to Alysanne, who tried to strengthen the Night's Watch thereafter.
The Sad, Short Life of Aerea Targaryen
Aerea Targaryen was a Princess; daughter of Aegon, who was murdered by his uncle Maegor. Aerea was the older twin to Rhaella Targaryen, who was rambunctious and bold (which was an issue because she had been given to the Faith in an effort to smooth over Maegor's crimes). Aerea was shy and prone to tears in her youth, but after her uncle Jaehaerys was crowned, she seemed to become brave and rambunctious herself, while Rhaella became shy and withdrawn. There were whispers that she was switched with her sister.
She spent the next few years in King's Landing, where she eventually reunited with her mother Rhaena. The two did not really know each other, however, and Aerea grew resentful when Rhaena moved the two to Dragonstone. The two quarreled with one another often, and after one fight, Aerea did the unthinkable: she claimed Balerion as her own. She was only 13, however, and unable to control the dragon. For a year, she disappeared.
When she returned, it was discovered she had been in Valyria, and that the tales of a curse upon the place were not exaggerated. Her clothes were ragged, she was emaciated, and worms were crawling underneath Aerea's skin. Smoke emanated from her orifices. The worms were cooking her from the inside, boiling her eyes, and she died when those attending to her placed her in cool water in an effort to ease her suffering. Those who attended to her refused to repeat what she had told them of Valyria, but King Jaehaerys forbid travel to Valyria thereafter.
These incidents are just a few, short episodes in the era before House of the Dragon. There are countless more stories to be told within the show - George RR Martin has stated the 'sweet spot' for the Dance of the Dragons plot line is four seasons, but the show may turn into an anthology afterwards. Perhaps some of these stories can show up on screen.
House of the Dragon's season finale airs Sunday at 9PM EST on HBO and HBO Max.