Given its very strategic location in the east Med, much like Malta's further West, it has been invaded more times than we could mention, or even know about. Romans, Greeks, Ottoman, Byzantine, Brits. They've all had a piece of it

In living memory, it was British (as part of the Empire), then made it's own sovereign state, bar the 2 UK bases, then a bit of a coup in the 70s caused some concerns with the Turks, who promptly tried to invade. They only managed to invade the north, and so we have a Turkish Republic of Northern Cyprus - not universally recognised by all countries - and Cyprus being the rest, excluding Akrotiri and Dhekelia which are the 2 bases. And a UN line between them, as the UN think this is a good hoot, and a great place to get sent.
As part of this, there was a bit of India/Pakistan type separation, with the Greeks being moved south and the Turks being moved North, despite them previously living side by side happily until this point. Additionally, Turkey active migrated people from Turkey to Cyprus to re-enforce their hold on the territory, which has caused ongoing friction, more so on the eastern side it seems.