How the Game of Thrones Dragons are Created

I've been re-watching Game of Thrones in anticipation of the Season 5 premiere in April. One thing that gets me is the computer-generated dragons. They really look great—like, movie-great, not TV-great. It's particularly interesting how much they interact with Emilia Clarke, who plays Daenerys Targaryen. How do they do that thing where Clarke pets a dragon on the head and reacts to the dragon's movement? What is she petting? This video explains, using a raw-visuals approach (no narration, just lots of images that explain all the layers that are put together to make a final shot).
What always gets me is when they go through the rendering passes, get the dragons perfect, and then add several layers of dirt and crap, then mess up the lighting. That's a key ingredient if you want "real" looking dragons.
Warning: Contains images of dragon violence against computer-generated goats. Many, many goats. (This also has some dragon-related spoilers for Season 4.)