Rhaegar is the eldest of three children born to Aerys and his wife/sister, Rhaella, along with younger siblings Viserys and Daenerys. With the dragons long extinct or near extinct, he is not a dragonrider like his ancestors but distinguishes himself as a knight.
Rhaegar marries Elia Martell and has two children with her, a son and a daughter. As his father descends further into tyranny and madness, Rhaegar causes further problems when he falls in love with Lyanna Stark. A civil war breaks out when the Starks and the Baratheons believe Rhaegar has abducted Lyanna, and it ends with the Targaryen dynasty overthrown and both Aerys and Rhaegar dead. The truth, however, is that Rhaegar and Lyanna were in love. Rhaegar had his marriage to Elia annulled and secretly married Lyanna, who died giving birth to their secret son, Aegon. It's revealed in the final season of "Game of Thrones" that Aegon was raised by the Starks as Jon Snow.