Waghar is the largest dragon
Waghar is the largest dragon in House Targaryen, and in her few current aerial scenes, the show fully demonstrates her immense deterrence.
Waghar is the oldest dragon owned by the Targaryen family in Family of Dragons, and Visania Targaryen rode it during the reign of King Aegon Targaryen in the years leading up to the episode.
Lanal Valerian owns Waghar
While Visania Targaryen has ridden Waghar in the past, in the timeline of Family of Dragons, Princess Lanal Valerian (Lana Brondale) owns her. We even saw her flying with her husband, Prince Damon Targaryen (Matt Smith), on their way back to Pantos.
Unfortunately, Lannar undergoes a traumatic birth in episode six, putting both her and her baby at risk, and she forces Waghar to end her pain with that all-important dragon phrase, "Dracarys."
Kolachue has a snake-like neck
Kolachue may not be the largest dragon in the family, but he is longer than most other dragons due to his serpentine neck. He also has bright red scales, which makes him look very unique. His original owner was Eamon, son of King Jehris Targaryen I, who later died at the hands of pirates in the Mir Strait.
Damon Targaryen rides Kolakhue
The owner of Kolakshue is the notorious prince Damon Targaryen, who constantly betrays his brother in the play. He even takes Dragonstone (and a dragon egg) for himself along with his lover Mesaria (Sonoya Mizuno), and in episode two when people try to drive Damon out of the castle, he uses Kolachue to intimidate Sir Otto Hightower (Rhys Evans) and his troops. Although his actions were not successful because of the appearance of another dragon.
Syracus has yellow scales
Thankfully, Otto and the soldiers were supported by some of their own dragons, and Syracus was a yellow dragon similar in size to Korakhue. She is a much younger dragon compared to dragons like Waghar and Kolachue, but her ferocity is no less. This is also one of the reasons why the Great Demon King flinched when he met her on the bridge of Dragonstone. Although this may also be related to the people who rode Syracx.
Rhaenyra Targaryen rides Syracx
Yes, Princess Rhaenyra Targaryen (Millie Alcock) rides Syracx. The show shows this mighty girl riding a yellow dragon in the first two episodes. She dares to confront her uncle Damon, which may be one of the reasons why he was attracted to her in the first place.
The elder Rhaenyla (Emma Darcy) later gave one of Syracx's eggs to Emond Targaryen (Leo Ashton), son of Alison Hightower (Olivia Cook).
Wormax is a little dragon
Vomax is much younger than most of the dragons in this series, nor is he as tall as Waghar, Korakhue, and Syracs. He first appears in episode six, when the dragon keeper leads him to the children of Rhaenyra and Alison. Womax also has a unique appearance, he has green scales and a red backbone, but he can't fly into the sky yet.
Targaryen learn how to control Vomax
Vomax belongs to Jakaris Targaryen (Leo Hart), who learned how to use the commands of "dracarys" from the dragon keeper and is still learning how to control the young dragon. The dragon keepers were clearly rewarded, because Vomax was tasked with roasting sheep on order, poor goats ...
Haiyan took part in the war on the Stone Steps Islands
Sea Smoke is another dragon of the Targaryen family, but he is given to the Valerian family because Princess Rhaenys Targaryen (Eve Best) is married to Colis Valerian (Steve Tuscent), aka the sea serpent. Sea Smoke is a silvery-gray dragon who proved to be a key weapon in the Stone Steps Archipelago War.
Sea smoke was ridden by Lanino Valerián
Sea smoke belongs to Lanino (Thor Knight), son of Rhaenys and Collis, who saved Damon when he confronted the crab feeders and their army during the Battle of the Stone Steps archipelago.
Lanino eventually married Rhaenyra, and they were still together after a time jump, with John McMillan taking over the role. Although the father of their child was actually Sir Harwin Strong (Ryan Cole).
Melia is also known as the "Red Queen"
Melias is a very large red dragon who has appeared several times in Family of Dragons, the first time being when she travels to King's Landing, next to Seasmoke and Lanino Valerien.
But Melias is becoming a key weapon against Alison Hightower and Aegon Targaryen (Tom Green-Carney). And her explosive appearance in the coronation scene of the Dragon's Lair in episode IX is a sign of an era.
Rhaenys Targaryen rides Melias
Melias was ridden by Lanino's mother, Rhaenys, a cousin of King Viserys Targaryen I. She and Corliss had been suggesting that the king marry Lannar when she was 12 years old. Thankfully, he refused, instead marrying Alison.
It is worth mentioning that Rhaenys also warned Rhaenyra that she was in danger as heir to the Iron Throne, as most men did not want a woman to rule Westeros.
Rhaenys proves that she is just as dangerous as the rest of House Targaryen when she disrupts Aegon with Melias in episode nine.
Dream Fire was for Berron Targaryen
Finally, there is the dream fire. If she doesn't get noticed right away, don't worry because she's only briefly mentioned at a small council meeting in the second episode. Dream Fire is mentioned because the Great Demon King stole one of her eggs, which was intended for Rhaenyra's little brother Berron Targaryen, who died shortly after Queen Emma gave birth to him in the first episode.
Princess Helena will ride the dream fire in the future
Viserys and Alison's daughter, Princess Helena (Evie Allen), has not yet become the protagonist of Dragon Family, but according to 2018's Game of Thrones author George R-R. Martin's Blood and Fire, she will eventually become the one riding the dream fire. No spoilers, but Helena would be an important part of the Civil War, where she was dubbed the "Dragon Dance" and tore apart the Targaryens.