Rhaegal

Rhaegal is one of the dragons born on the Dothraki Sea, along with Drogon and Viserion. Commanded by Daenerys Targaryen, he was named for her brother, Rhaegar Targaryen. He is distinguishable by his green and bronze colored scales, and his yellow-orange colored wings.

Physical appearance
Most of Rhaegal's scales are emerald green, with a few bronze scales on the underside of his neck and tail. His frills and wings are yellow-orange colored, becoming a darker green near the wing-bones.

Season 1
He is born along with his two siblings after Daenerys has their eggs placed on the funeral pyre erected for her deceased husband, Khal Drogo. As she rises unharmed from the ashes of the pyre on the morning following the funeral, he is cradled by Dany at the time.

Season 2
Rhaegal is taken along with his "brothers" to Qarth. He is stolen by Xaro Xhoan Daxos, along with Drogon and Viserion. As Daenerys enters the House of the Undying to retrieve them, she eventually finds her three dragons chained. Pyat Pree attempts to chain her with magic, claiming that her dragons make his magic strong, and that she makes them stronger, thus she will stay with them for an eternity. She whispers to her dragons the command of fire, and the three of them burn Pyat Pree alive, releasing his magic.

Season 3
Rhaegal, along with his brothers, accompanies Daenerys on her journey from Astapor and Yunkai. When Daenerys has a meeting with a Razdal mo Eraz, of the Wise Masters of Yunkai, Rhaegal hisses at the slaver along with his brother Drogon when he comes too close to Daenerys. He then fights over a piece of meat with his brothers when Daenerys makes a show of force to intimidate Razdal. After Daenerys frees the slaves of Yunkai, Rhaegal takes to the sky with his siblings at Daenerys's command; a show of both power and freedom.

Season 4
Rhaegal is seen with his brother Viserion fighting over a dead lamb. Drogon, who is now visibly bigger than them, quickly takes the lamb as his brothers squeal for him to share. He sets the corpse down and the three begin to eat. In response to Drogon's killing of a three-year old girl, Daenerys leads Viserion and Rhaegal into the catacombs of Meereen, where she chains them up.

In the books
In the A Song of Ice and Fire novels, Rhaegal is much the same. In some ways he is essentially the "middle brother" of Daenerys's three dragons: Drogon is larger than both of his brothers and the most aggressive, while Viserion is the best behaved towards other people besides Daenerys. Rhaegal, meanwhile, is not as aggressive as Drogon but is also not as friendly as Viserion.

Daenerys named Rhaegal in memory of her older brother Rhaegar, the last great champion of House Targaryen.