Armenia-Azerbaijan: What's behind the Nagorno-Karabakh conflict?

Fighting has erupted once more between Armenia and Azerbaijan, two former Soviet Union republics in the Caucasus region.
At the heart of the decades-old conflict is the Nagorno-Karabakh region. It is recognised as part of Azerbaijan, but it is controlled by ethnic Armenians.
The countries fought a bloody war over the region in the late 1980s and early 1990s. Although they declared a ceasefire, they have never managed to agree a peace treaty.