As TS says, the main route DXB-Europe is the gulf, Kuwait, Iraq, Turkey, Black Sea, Bulgaria.. Since the Crimea debacle, Simferopol airspace has been closed, however, Ukraine and Turkey control roughly half the Black Sea each, and before the closure, depending on your destination you could routinely be planned through southern Simferopol airspace, but not Kyiv.
The alternate route DXB-Europe is through Iran initially, then Turkey, Black Sea, Bulgaria etc with the same chance of proceeding through Simferopol.
Europe- DXB is the same as above, with the additional alternate of proceeding through the Turkey/Cypress/Syria/Jordan quadrant of 'war and no mutual communications', before entering the relative sanctuary of Saudi, except that Syrian airspace remains closed. It takes a strong jetstream, but from Italy I have also recently been routed from Turkey into Alexandria while Damascus has been closed.
Its a big and dangerous world out there.
Wiki lists 11 current ongoing conflicts with over 1000 deaths, and 34 ongoing conflicts with less than 1000 deaths in the current year. As a bog standard line driver for EK, I have personally overflown all but 4 of those countries in conflict, and EK regularly lands in countries involved in approximately 33/45 of those conflict zones.
Should we be concerned? Is getting your hands on a soviet-era SA-11 ground-to-air missile and shooting down a civilian airliner the new black? Or do we have a couple of dickheads who had one too many vodkas in the sunshine? A look back through the last weeks news shows a couple of low level military aircraft being shot down, but certainly no international outcry from IATA, ICAO, EASA, NATO, the USA or anyone in fact suggesting any threat to civilian airliners. Should we now avoid all countries involved in some sort of conflict?
I don't have the answers. They are a long way above my pay grade.
I'm heading back to the coal face tomorrow. There is a strong chance I'll be flying by the conflict zone. The target engagement zone for aircraft on the SA-11 is reported at approximately 23 NM. Not that I expect to be planned any closer, but tomorrow, the words 'reasonably wide berth' come to mind.