Rhaegal

Rhaegal is one of the three dragons born in the wastelands beyond Lhazar, along with Drogon and Viserion. He is named after Daenerys Targaryen's eldest brother, Rhaegar. He can be distinguished by his green and bronze colored scales, and his yellow-orange colored wings. Rhaegal is also the personal mount of Jon Snow.

Season 1
Daenerys is given three dragons eggs by Magister Illyrio Mopatis on the occasion of her wedding to Khal Drogo. She is drawn to these eggs and always keeps them in a chest with her. Viserys tries to steal them but is stopped by Ser Jorah Mormont.

Rhaegal 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. Daenerys enters the House of the Undying to retrieve them and 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 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 and pits Drogon against the fleet assembled by Astapor, Yunkai, and Volantis, Rhaegal and Viserion break out of the catacombs and join their mother and brother in destroying the the slavers' fleet with dragon fire, decisively breaking the Second Siege of Meereen. This defeat marks the end attempt to reintroduce slavery to Meereen.

Some time later, Rhaegal and his brothers accompany their mother and her large army on a voyage to retake Westeros by soaring above the armada.

Season 7
Rhaegal and his brothers fly ahead of their mother as she lands on Dragonstone. They investigate the island as Daenerys enters and secures the castle.

Later, Daenerys tells Jon that both Viserion and Rhaegal were named for her deceased brothers, Viserys and Rhaegar, respectively. Rhaegal and his brothers fly North of the Wall to help battle the White Walkers and the army of the dead that are advancing on Jon Snow and the others during their Wight Hunt. During the battle, the Night King fatally wounds Viserion with an ice spear to the neck. Rhaegal swoops after him in a desparate attempt to help, but it's too late; he can only cry in despair as Viserion crashes through the frozen lake and slowly sinks into the waters.

Daenerys brings Rhaegal to the Dragonpit, as a show of power: he circles overhead as she lands on Drogon's back. Bringing Rhaegal proves to be a minor error, however, as Cersei Lannister notices Viserion's absence and correctly concludes that something has happened to him, brushing off Jaime's suggestion that the third dragon is guarding the fleet.

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. By the time he and his mother reached Westeros, many of the scales on Rhaegal's dorsal side, and most of those along his frills, had turned almost black, while his neck was striped with bright green and black.

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 on-screen (alongside Viserion's name) in Season 5 episode 1, "The Wars to Come".

Daenerys refers to her three dragons as "brothers", but as the exact origin of the eggs is never addressed, there is actually no 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 (even if they are all from the Shadow Lands, that region is at least as large as Dorne). She may call them "brothers" more in the figurative sense that they were raised together.

In the third novel, Rhaegal has grown to the size of a small dog, like Viserion, a bit smaller than Drogon. At one occasion he tries to snatch a piece of meat from Drogon, and Daenerys chides him for his greed.

During the fifth novel, Daenerys is so busy ruling Meereen, that she neglects the dragons. Like any wild beast that is left to grow without proper training, all three grow savage and unrestrained; first they prey on sheep and goats, causing significant losses to shepherds. Only after a little girl is killed by Drogon, Daenerys realizes the dragons pose a great danger to her subjects, and must be kept locked in a makeshift dragon pit, large enough to hold 500 men, inside the Great Pyramid.

Viserion is easily restrained, but Rhaegal is not, perhaps because he hears his brother raging in the pit. The servants have to cover him with a net of heavy iron chain as he basks on the terrace, and he fights so fiercely that it takes three days to carry him down the servants' steps, twisting and snapping. Six men are burned in the struggle. Drogon flies away.

As the Yunkai troops and their sellswords draw closer to Meereen, Ben Plumm urges Daenerys to to use Rhaegal and Viserion, but she reluctantly declines for a reason she cannot reveal - that she has lost control over them. As a result, the Second Sons switch sides.

Daenerys has Viserion and Rhaegal fed and visits them occasionally. As time passes, they break their chains and dig holes in the walls, though they still cannot exit the pit. When Daenerys comes with Quentyn Martell to visit them, she becomes worried that eventually they will break through the walls.

After Daenerys and Drogon leave Meereen, Quentyn seeks to steal Viserion and Rhaegal. The attempt costs his life (while attempting to whip Viserion into submission, Quentyn turns his back to Rhaegal and the dragon burns him alive), and the dragons finally become loose.

Viserion and Rhaegal terrorize the city, killing and eating people. They destroy the pyramid of Hazkar, then make the pyramids of Yherizan and Uhlez their lairs. Many of the Meereenese who reside in those pyramids are killed, either by the dragons' fire or crushed under the debris; the survivors find themselves homeless and penniless. Hundreds of people flee the city for any refuge that will have them; many others have lost all hope. In order to minimize the danger the dragons pose, Ser Barristan Selmy orders to fill the fighting pits with large amounts of sheep and bullocks, what seems to satisfy the dragons and make them less eager to feast on human flesh.

While making plans for the battle against the besieging armies, Selmy takes into consideration that Viserion and Rhaegal will undoubtedly arrive at the battlefield, drawn by the noises of battle and scent of blood, and probably attack both parties indiscriminately. Selmy hopes, though, that the sight of the dragons will demoralize the enemy troops.

During the ensuing battle between the defenders of Meereen and the besiegers, Viserion and Rhaegal are flying overhead. At the camp of the Second Sons, Tyrion watches Rhaegal circling above the bay, where the ironborn fight the besiegers' fleet, banking and turning as longships and galleys clash and burn below him.