Quick Answer: Game of Thrones' three-headed dragon is a storied prophecy in House Targaryen. Daenerys' ancestors, Aegon, Rhaenys and Visenya, rode dragons and conquered the Seven Kingdoms. As Daenerys has mastered riding Drogon, who will join her and ride Viserion and Rhaegal? Fans theorize that two more characters will join her in becoming dragon riders and help her win the Iron Throne. But who could those people be? The most common theory is Tyrion Lannister and Jon Snow. Tyrion is now Daenerys' trusted advisor, and we've seen that he has a way with the dragons. And Jon Snow, if the R+L=J theory is correct, if half Targaryen, making him an obvious candidate. If this is the case, these three will unite three of the greatest houses in Westeros: Stark, Lannister and Targaryen.
Season 6 of Game of Thrones (2011 - ) is wrapping up this upcoming Sunday, and with all of these new alliances forming, the question of the three-headed dragon prophecy is more important than ever. Fans of the books should be familiar with the prophecy, but it isn't talked about as much on the show. Let's break down what the dragon prophecy is and who it could affect.
Emilia Clarke as Daenerys Targaryen
As fans of the show will know, House Targaryen's banner features a three-headed dragon. Not only that, but Daenerys has three dragons: Drogon, Viserion, and Rhaegal. Back in Season 2, Arya speaks of Aegon and his sisters, Rhaenys and Visenya, a moment that is captured more extensively in the book. Aegon, Rhaenys and Visenya were dragon riders. Together, they led the Targaryen army to countless victories, conquering Westeros and becoming its ruler.
At the end of Season 2, Daenerys enters The House of the Undying in order to get her dragons back. Daenerys has many visions, one of which is of her brother, Rhaegar. He says, "The dragon has three heads." Though this could be taken literally, it's more likely a metaphor for Daenerys. The vision suggests that two others will join her as dragon riders and help her conquer Westeros. The question is, who? As we all know, Game of Thrones fans are wont to theorize. Here are two characters that fans speculate will join Daenerys and become dragon riders.
1) Tyrion Lannister
Peter Dinklage as Tyrion Lannister
Tyrion Lannister has always been an underdog. Though a family outcast and a subject of hatred by many, Tyrion has always remained clever and resilient. He recently travelled across the Narrow Sea and befriended Daenerys Targaryen, the Mother of Dragons herself. This season, he has been ruling in her stead while she's away. He's had to take on a number of responsibilities, including the occasional bit of dragon maintenance. As Viserion and Rhaegal were in chains, they were growing restless and refused to eat. However, Tyrion understood that dragons do not do well in captivity. Earlier in the season, Tyrion managed to sooth and unchain the beasts using only his words. Up until this point, Daenerys had been the only one to truly get close to them without fear of getting hurt. Tyrion's calm and fearless handling of the dragons suggests that there may be more interaction with dragons in the future.
In addition to proving his aptitude for dragon-soothing, Tyrion's relationship with Daenerys has developed this season. He's become her righthand man and trusted advisor. Moreover, he knows how to play the Game. Daenerys needs a Westerosi -- someone who's truly been a part of the Game of Thrones -- to show her the ropes. It's not unlikely that Daenerys would eventually trust Tyrion enough to allow him to ride either Viserion or Rhaegal. One can't deny that there would be something supremely satisfying about Tyrion mounting a dragon. Imagine the Imp, a man so hated and ridiculed by the people of King's Landing, riding in on the back of a dragon.
2) Jon Snow
Kit Harington as Jon Snow During the Battle of the Bastards
Daenerys and Jon may have never met -- in fact, they have been on opposite sides of the world for the entire duration of the show -- but many fans are convinced that Jon is destined to be a dragon rider. But how is this possible? It all goes back to Jon's parentage and R+L=J. According to the popular fan theory, Jon's actual father is Rhaegar Targaryen and his mother is Lyanna Stark. If this theory is true, that would make Jon a Targaryen, and therefore heir to the Iron Throne. What's more, it would make him Daenerys Targaryen's nephew. As many know, it isn't uncommon for the Targaryens to interbreed, often marrying their siblings. An aunt/nephew relationship wouldn't be unheard of. And if he is truly a Targaryen, there's no doubt that he would become the next dragon rider. He may even rule the Seven Kingdoms by Daenerys' side. If Jon is half Targaryen half Stark, this would guarentee a strong alliance between the two houses, as well as peace between the North and the rest of the land, something we haven't seen since Season 1.
Kit Harington as Jon Snow and Peter Dinklage as Tyrion Lannister
If these two truly do become the next dragon riders, they will be uniting three of the largest Houses in Westeros: Targaryen, Lannister, and Stark. This unheard of combination would definitely bring some much needed peace to the land. But there are, of course, other theories out there. Some believe Daario will be the next dragon rider, and though he is close to Daenerys, it's not clear whether or not he's the wisest option. While she is romantically involved with him, she knows he cannot rule by her side. It would be nice for Daenerys, but not for the Kingdoms. Others think it could be Jorah, and if he recovers, he very well could be. He's wise, he loves Daenerys, and she trusts him. However, how it would look to the people if a man who once spied on Daenerys was rewarded with a dragon? And as we are almost certain that there is no cure for Greyscale, the chance will likely not be given to him. But if he was to become a dragon rider, I wouldn't complain.
Daenerys has recently formed a new alliance with Yara Greyjoy, and it is already very strong. Could she be the next dragon rider? It's doubtful. While their bond is strong, Yara will become the Queen of the Iron Islands, and Daenerys will want her riders by her side. That being said, with this new alliance, she finally has the ships to travel to Westeros and take back the Iron Throne. And once she reaches the Seven Kingdoms, the sooner and more likely it is that she will meet Jon Snow. That is the best situation we can hope for. Daenerys Targaryen, Tyrion Lannister, and Jon Snow are all outcasts who have faced tragedy. They are loyal and intelligent, and together they would bring peace and justice to the Seven Kingdoms. The reveal of the remaining dragon riders still remains uncertain, but Tyrion could be revealed as soon as the Season 6 finale. Let's just keep our fingers crossed until Sunday.