Princess Rhaenyra is the only surviving child of Viserys I and his first wife, Queen Aemma, and she is Viserys's intended heir. She, too, is a dragonrider, bonded with the dragon Syrax. She has no full-blooded siblings, but multiple half-siblings through her father's second marriage, which launches the civil war.
Rhaenyra first marries Ser Laenor Velaryon, with whom she has three sons (at least, in name) before she is widowed. Her second marriage to her uncle Prince Daemon Targaryen produces two sons and a daughter: Aegon, Viserys, and Visenya. After her father dies, Rhaenyra is not even told about his death until after her half-brother Aegon claims the throne. The resulting battle between Rhaenyra and Aegon's claims explodes into the civil war.
The Targaryen line ultimately continues through her and Daemon's descendants.