It all started when Greece faked the statistics about their economy in the mid-90s and probably before as well, they did it because EU members are supposed to keep their new debt in a given fiscal year below 3%, Greece was at 4 or 5%, and counting. They lived pretty well for a while when they got connected to the money pump that is the European Union, until about 2004 when their economy data went downwards again, and then the financial crisis of 2007 hit them very hard. Masses of people lost their jobs which led to a near-breakdown of their domestic market, which in turn became a probem for foreign investors from France and Germany who started to withdraw their money. It's no secret that these investors took advantage of the corrupt circles of industry leaders, investment bankers and politicians, they milked a pretty cent out of the country and still do.
A lot of their problems are based on corruption within the government and the cabinet that is manned by a bunch of inept populists. They have huge problems collecting taxes, a lot of Greeks haven't paid them for years, if not decades. Everyone is doing his thang and only cares for their personal wallet, this includes keeping dead people alive on paper in order to still get the pensions, which is a popular sport in Greece and until recently went on more or less undetected until the new financial crisis highlighted these any many other problems.
And of course it's Germany's fault that Greece is about to go belly-up, that goes without saying...