I'm sorry to say but the mainstream press coverage, reflected in most comments, is horrible. You've stuck with the vandalisms (limited practically in Athens and Thessaloniki, targeting overwhelmingly banks and multinationals) and you've missed the real issues.
It's not really a movement (yet), it is not the paranoid act of either some spoiled brats or some anarchist bombers living in somekind of 19th Century utopia or some thugs who don't need any excuse to loot. It's all this AND a massive mobilization of youngsters (starting from 12-13 years old in some cases). I guess the foreign media don't show you the hundred daily protests, marches, sit-ins, rallies etc that take place peacefully (when not provoked by our beloved police who's already used 4.5 tons of tear gas - must be a WR!). For the time being it has been a long-due explosion of rage, proteic and irrational. Don't expect the mass to behave, don't look for political correctness from an angry mob. Moreover it's a complex social phenomenon than a mere question of public order. I have no clear answers, I'm still trying to figure out what happened.
Still, I can assure you the people engaged in somekind of violence (starting from throwing eggs or stones to the police) were not the few hundreds hooded anarchists, the so-called "known-unknown" of downtown Athens. To my great astonishment I've been told by people I never expected to be keen to this kind of activities stuff like "I'm going to clash with the cops" etc. The professional rioters were the protagonists of the first hours, but what happened next wasn't their work, let's be clear about it. This is a convenient mythThere is no anarchist underground in places you've never heard before, such as Kozani or Mytilini. . The truth is that there's something rotten in the kingdom of Denmark (or the Hellenic Republic) to push 15 year olds to besiege police stations. To reduce the whole thing into a chain of vandalisms by a bunch of thugs is a misunderstanding.
Of course, the murder of the child or the mounting police brutality was just the pretext, a detonator that led to serious, widespread outrage throughout the nation. What lies beneath is a chronic malaise and discontent, very vivid during the last years, particularly amongst younder generations. Please take in consideration what an explosive mix can create the conviction that "this is the first generation that will live worst than its parents" (repeated various times in Greece), an approaching economic crisis, economic conditions where wages stay low while prices have overriden the Europe Union average, the desesperation and angst of the "generation of 700 euros", a corrupt and clientelist political and party system, a scandal-striken government, a failed educational system, wide-spread lack of belief in the system (including among people shocked by the extent of violence), a culture of symbolic and material violence, feelings of nihilism among the younger generations, the existence of radical groups experienced in subversive action etc.
I hope that all this rage will be channeled into some kind of grass-root mass movement to empower younger generations that would push for serious reforms. If we, in Greece or elsewhere, continue to speak exclusively about a bunch of irreverent hooligans just to show our horror that "BSB", "Zara" or "Starbucks" were burnt down, we will miss the reality of a growing discontent.
Maybe that's "all Greek to you", maybe it won't be in the near future.

PS I'm Greek, I don't support violence, I consider protest a necessity in these times, I try to understand what's going on.

Maybe they are people who don't like it when the police shoot dead and 16 year old boy.
Rock on!