They were under control of the Ottomans from around 1452 (when Constantinople fell) to 1829. As far as Muslim rulers go, the Ottomans were pretty lenient. Also of note is the fact that the [heavily Muslim] Arabs are also strongly anti-Turkish/anti-Ottoman. Greece largely won its independence by itself.
The Greeks had the aid of western philhellenes, notably Lord Byron. The western governments were reluctant to get involved, but finally did. One key event was the battle of Navarino on Oct. 20, 1827, when the British, French, and Russian fleets destroyed the Turkish (Egyptian) fleet in the Bay of Navarino (SW Peloponnesus). In 1829 the Turks agrreed to complete independence for Greece, under very restricted borders (the Peloponnesus, some of central Greece, and the Cyclades). I don't know if the Greeks would have managed to achieve independence without outside help, but I'm not an expert on the subject.