Rhaegal

"Viserion? Rhaegal?"

- Daenerys Targaryen calling to her dragons.

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 named Zalla, Daenerys leads Viserion and Rhaegal into the catacombs of Meereen, where she chains them up.

Season 5
Daenerys finally decides to reenter the catacombs to attempt to regain control over her dragons. Rhaegal and Viserion, who have grown even larger during their time in captivity, immediately lash out and breathe fire at the sight of their mother who imprisoned them.

Some time later, Daenerys, reeling over the death of Ser Barristan Selmy, arrests the leaders of Meereen's great families and brings them to meet Rhaegal and Viserion. Rhaegal roasts one of nobles and tucks in, sharing the meal with Viserion. Her point proven, Daenerys leaves, sarcastically saying that she doesn't want to overfeed the dragons.

Season 6
In the Great Pyramid, Tyrion Lannister learns that Rhaegal and Viserion have not been eating anything ever since their mother had left. He decides to free them, knowing that they will be better off that way.

Accompanied to the entranceway by Varys, Tyrion ventures alone into the catacombs and encounters Rhaegal and Viserion for the first time. Despite their initial hostility towards him, Tyrion remains calm, assuring them he is a friend of Daenerys and only wants to help. He manages to earn their trust and unshackle them, all the while telling them the story of how he wanted a dragon for his nameday, only to be disappointed by uproarious laughter from his family and the cold truth from his father. Once free, the dragons immediately depart into the darkness behind them while Tyrion quickly exits the catacombs with Varys.

After Daenerys returns to Meereen, she breaks Rhaegal and Viserion out of the catacombs. Under her orders, the two dragons and Drogon destroy the slavers' fleet with dragon fire; breaking the Second Siege of Meereen. This defeat marks the end of Astapor, Yunkai, and Volantis' attempt to reintroduce slavery to Meereen.

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.

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

Rhaegal's name wasn't mentioned on-screen as of the end of Season 4, though it was stated in the Season 4 HBO Viewer's Guide, establishing that his name is the same in the TV continuity. His name was finally stated in on-screen dialogue in Season 5 episode 2, "The House of Black and White".

Daenerys refers to her three dragons as "brothers", but there is actually no specific reason to think that their eggs were all laid by the same dragon, or if the three eggs were even found in the same place or gathered individually. She may call them "brothers" more in the figurative sense that they were raised together.