I know about the current dispute with Nagorno-Karabakh, but I've read that those 2 culture have at least a century-old beef with eachother.
How come? How did it start?
This immediate conflict was sparked with a collection of signatures in late 1987 by the government of the Autonomous Republic of mountainous Karabakh which called for a “reunification” with Armenia which was supported in demonstrations in Armenia. Tom de Waal tried to reconstruct the succeeding escalation in his 2003 book “Black Garden”.
According to the “deep freeze” theory of conflicts in the USSR it goes back to the immediate pre-revolutionary period when, starting with February 1905, there was a spiral of violence which took several thousands of lives on both sides. Here the initial reason is obscure.
Sectarian intellectuals tend to look for reason even deeper in the antiquity. To get the Armenian narrative get the work of Shagen Mkrchan (f.e.«Historical Monuments in Mountainous Karabakh», Erivan: Parberakan, 1989). The Azeri answer is avaible on garabagh.net.
For both sides the basic idea is that the other ethnic group has been maliciously planted into the region on purpose by some foreign empire to steal delicious clay.