From WIkkipedia:
During a demonstration in front of the Parliament in 2001, a Molotov cocktail was thrown at one of the guardhouses. In no time, the wooden construction was engulfed in flames. The Evzone standing next to it did not even blink his eyes, let alone move, until the officer in standard uniform came and gave him the order to move. With a scorched and partly smoking uniform on one side, the Evzone did so.[3]
In January 2010, a makeshift bomb was placed 20 meters from where the Evzones guard the Tomb of the Unknown Soldier, at Syntagma Square. Although the police informed the Evzones of the imminent threat, the Guards refused to leave their posts and remained on guard while the bomb exploded
Ive been there a few times.......those guys are like statues.......