There was a civil war that started in 1946 between Royalists and Socialist partisans (DSE).

The DSE were supported by Yugoslavia and the Greeks received heavy military and financial aid from the UK (Until 1947 when the US took over due to the UK's withdrawal).

Yugoslavia's support for the war was undermined when the USSR called for its end. Eventually Tito gave in to the USSR's demands and closed its border to Greece, cutting off supply lines for the socialists. This impacted the DSE greatly, demoralising its command and creating infighting.

This, on top of the US hugely stepping up its aid to the Greek government (Marshall Plan, Truman Doctrine) and a lack of manpower on the socialist side, eventually lead to their defeat in 1949.

After the conflict the population was still polarised between left and right, and after a number of incidents and crises a group of right wing army officials overthrew the government and set up a military junta that lasted until the mid 1970s.

During the cold war Greece was heavily aligned towards the West, and had strong diplomatic ties with the UK. Stalin and subsequent leaders generally considered it to be firmly in the western sphere of influence, despite it being in the Balkans.

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http://en.wikipedia.org/wiki/Percentages_agreement#mediaviewer/File:Percentages_agreement2.jpg

http://en.wikipedia.org/wiki/Percentages_agreement

Inside Hitler's Greece: The Experience of Occupation, 1941-44

Is a great book for understanding the underlying cause of the Greek Civil War that followed the nazi occupation.

"Having already privately agreed with Stalin that Greece lay in Britain's sphere of influence, he was in no mood for compromise with the Left. 'I fully expect a clash with EAM,' Churchill noted as early at 7 November, 'and we must not shrink from it, provided the ground is well chosen.' One week later, Churchill instructed Scobie to make 'maximum use' of the troops at his disposal 'to show the flag'. He was to ensure the security of Athens, if necessary by declaring it a military area and ordering all ELAS troops to pull out. Scobie's instructions closed on an uncompromising note: 'In the event of an attack on British troops, or an attempted coup d'etat, you have full authorisation to use such force... as may be required to crush ELAS.' (p. 365)

Also it was considered to be in the British sphere of influence by stalin after he and Churchill made side agreements during the Yalta conference. One of the main reasons the soviets did not push more support towards the Greek socialists