|The title of this article is conjecture based on information revealed in the A Song of Ice and Fire novels and may be subject to change.
Balerion is the name given by Daenerys Targaryen to the ship she purchases to leave Qarth along with her khalasar and dragons. It is named after Balerion, the dragon of her ancestor Aegon I Targaryen.
Daenerys Targaryen and her followers arrive at the city of Astapor in Slaver's Bay on the Balerion. As they approach, a few hours away from the harbor, her dragons fly in circles around the ship and catch fish from the sea.
Behind the scenes
The ship was actually a re-use of a prop ship designed and built by Gemma Jackson's production team for Season 2, which appeared on fire during the Battle of the Blackwater (possibly the same prop ship used for Black Betha). The ship was constructed in Banbridge, Northern Ireland, and it wouldn't have made sense to move it for scenes entirely set on the ship, so all of Daenerys' scenes on the ship were filmed in Northern Ireland. This makes it the only scene Emilia Clarke filmed in Northern Ireland instead of Morocco for Season 3. Filming for the scene took only one day.
In the books
In the A Song of Ice and Fire novels, Illyrio Mopatis sends three ships - Saduleon, Joso's Prank, and Summer Sun - to Qarth to bring Daenerys Targaryen back to Pentos. Daenerys renames the three ships after the three dragons of her ancestor Aegon the Conqueror. The great cog Saduleon is the one renamed Balerion.