Princess Rhaenys Targaryen is known as the "Queen Who Never Was." She is the daughter of the late Prince Aemon Targaryen and his wife, Jocelyn Baratheon. Her father, Aemon, was the son and heir of Jaehaerys I, and she was presumed to be her father's heir in turn. As with other Targaryens, Rhaenys is a dragonrider, riding the "Red Queen" Meleys.
However, when her father died before he could ascend to the throne, Jaehaerys had to choose between two possible heirs: Rhaenys, or Aemon's brother (Rhaenys's uncle) Baelon. Jaehaerys chose Baelon, who also died. Jaehaerys decided to call together a Great Council where everyone's claims for the throne would be heard. The two best claims were Rhaenys's and that of Baelon's son, Viserys. Overwhelmingly, the lords choose Viserys because he's a man. She and her husband Corlys Velaryon live with that slight forever.
Rhaenys and Corlys share daughter Laena, who marries Rhaenys's cousin Daemon, and son Laenor, who marries Rhaenyra and would have become the queen's consort if everything had gone to plan. It's one of the places where the Targaryen tree gets the most twisted, since everyone in these marriages (besides Corlys) is closely related.