How were the Turks able to invade half the island in the 1970's? 
Why didn't the Greek army kick them off?
The Turks have more-or-less ruled Greece since the fall of Rome. Greece was an integral part of the (Orthodox Christian) Byzantine empire, with its capitol in Constantinople. Mainland Greece & most of the islands were repopulated with Slavic and Turkic peoples from other parts of the empire -- for reasons economic and otherwise. When the Eastern Empire fell and the Ottoman Muslims took over, the Turkish grip on Greece loosened somewhat. But the Ottomans were still the de-facto rulers of Greece, and
they considered it a second-rate province. Its Christian denizens were treated accordingly.
...In the 19th century, with European help, the Greeks waged a war of independence & installed a German/Bavarian king. The monarchy has since been deposed.
Long story short: The Greeks have a long, long history as subjects of foreign rulers. Greek 'independence' is a relatively new concept -- for the vast majority of the past 2000 years, they've been a Turkish territory. Ironically, they were also ruled by German nobility.
