Game of Thrones has always been a visually impressive show, even by HBO's standards. The show's dragons are a big part of the show's aesthetic, and due to their rare appearances and quick growth they more or less have to be created from scratch for each appearance. Season five required something a bit more intricate to make them believable.
"The team began with a Technodolly — a motion-controlled crane with a 15-foot-high arm that moves in different directions while its base rolls along a track. The telescopic arm usually holds a camera, but instead the crew mounted a flamethrower that could shoot as far as 50 feet," TV Insider reported. "'Standing 50 feet away from the dragon fire, you could get a nice tan,'" executive producer D.B. Weiss says."
The nice thing about this rig is that its movement was both precise and repeatable; they knew exactly what it would do, and when. "This made it safer for the stunt team and more efficient for production, as both always knew exactly where the 'dragon' and his fire would be," the article says.
The rest of the story is worth reading for more insight into how it's done, and the challenges of acting next to something that looks very different on set, if it exists at all, for star Emilia Clarke. By mixing practical and computer generated effects the dragons are given an extra layer of reality; the dragons may be fake, but the fire and how it interacts with everything around it is very real.
You can read our thoughts on the first four episodes of season four of Game of Thrones right now, and of course it's worth watching how bad of a dinner guest Jon Snow would be in real life.