Wings of Fire: The Dragonet Prophecy (series) by Tui Sutherland

I really liked the first book and have read the second and most of the third. Even though these are aimed for a YA audience, the complexity of the story, the subtlety of the politics and the nuances of the plot mean that they will appeal to a wide audience. Readers who like action and adventure? Check. Resders who like characters and relationships? Check. Readers who like a long complex saga involving history and politics? Check. 

I will say that there are a few places where they get a bit gritty and violent. Not all of the dragons are nice. And some dragons die, not always in nice ways. Really sensitive readers might want to be aware.

After the first set of six books is finished, there is a further series.