Why House Targaryen came to the island of Dragonstone is unknown, since Old Valyria was at the height of its power and the center of the civilized world, which ended at the Narrow Sea. Westeros was a filthy backwater with seven kings squabbling over borders and minor glories. Dragonstone's only export is Dragonglass.
The Targaryens built a castle on the island. Some claim that they used sorcery, though in fact they had brought an army with them. Still, Dragonstone castle is very strange, built with advanced techniques of Valyrian stonemasonry which have since been lost. Soon after, the Doom of Valyria took place, hence they were prevented from returning to their home. Aegon I Targaryen realized that Westeros was ripe for conquest, perhaps a new Valyria.
Dragonstone proved the perfect starting point for Aegon's invasion of Westeros. The Blackwater Bay granted easy access to the continent. The lands around the mouth of the Blackwater River were disputed by three kingdoms: The Reach, the Iron Islands (who also possessed the Riverlands at the time), and the Stormlands. But their capitals were far enough away that none of them could agree on whose problem he was, out there in the borderlands, until it was too late and the Targaryens had already established a well-defended beachhead. With the bay to the east, the river to the south and open fields to the north and west, the location was impossible to take by surprise. Aegon built a stockade on a hill there for his army, which after the war he would expand into the new capital city of King's Landing. The Doom had taught the Targaryens the value of refuge, however, and after the War of Conquest Dragonstone became the seat of the crown prince and heir to the Iron Throne.
Three hundred years later, Robert Baratheon rebelled against the Iron Throne and House Lannister slaughtered the Mad King Aerys II Targaryen and his royal family. Robert dispatched his brother Stannis to kill the last surviving Targaryen children, Viserys and Daenerys. But before Stannis arrived, a loyal knight had smuggled them across the Narrow Sea.
Blinded by his hatred for the Targaryens, Robert blamed Stannis and stripped him of Storm's End, giving him Dragonstone in its stead. Robert would remind Stannis of the island's royal pedigree whenever Stannis demanded his rights restored.
With Robert dead, Stannis is the rightful king of Westeros. The usurpers and traitors will sit on the Iron Throne, and from Dragonstone Stannis will be the dagger at their throat.
- King Aegon I Targaryen, the "Conquerer"
- Queen Visenya Targaryen
- Queen Rhaenys Targaryen
- King Robert Baratheon (mentioned)
- King Aerys II Targaryen, the "Mad King" (mentioned)
- Lord Stannis Baratheon
- Prince Viserys Targaryen
- Princess Daenerys Targaryen (mentioned)
- Ser Willem Darry (indirectly mentioned)
- Dragonstone (island)
- Dragonstone (castle)
- Old Valyria
- Blackwater Bay
- The Reach (mentioned)
- The Iron Islands (mentioned)
- The Stormlands (mentioned)
- King's Landing (mentioned)
- Storm's End (mentioned)