Rec: the Temeraire series (fantasy)
There are four books in this series, written by Naomi Novik, so far: Temeraire (published in the US as His Majesty's Dragon), Throne of Jade, Black Powder War and Empire of Ivory. I must also praise the design of the covers on the new UK editions (linked to from this post) which I feel are very much in keeping with the novels themselves.
Essentially, the premise is that dragons are real and can communicate with humans; the series is set in the time of the Napoleonic wars and both France and England (not to mention other countries, met later on during the series) have dragons as part of their military forces. Those who work with the dragons are something of a law unto themselves, not always following the strictures of polite society - there is, for example, one particular breed of dragon who will only accept female captains, so the aviators include a number of women.
The first book is about the eponymous Temeraire, who is a dragon, and his captain Laurence - how they meet, their training together (since Laurence isn't an aviator by trade) and early adventures. The second book sees them travelling to China, in search of Temeraire's heritage. Black Powder War is about Temeraire's return to Europe, while Empire of Ivory sees him heading south, to Africa, in search of a cure for a disease that has decimated the English dragons while they have been away.
Empire of Ivory ends with a real cliffhanger, so I'm looking forward to book 5, Victory of Eagles, which is out in the UK in August.