Historically, Greece was a poor country in Europe because it was the periphery of the Ottoman empire and therefore barely received investment.
Through the 20th century, the country went through pretty corrupt governments (one of them being a dictatorship).
When they joined the European market, it was already a very unproductive country in relative terms, which tends to force you into remaining in the periphery under normal market conditions; and their most educated citizens saw a very easy and profitable opportunity in just migrating out.
On top of that, the only sector of the Greek economy that had any sort of strength was tourism, which very rarely provides good wages.
By the 2007 crisis, they already had a dangerously high debt. Because they were, again, a tourism-focused economy, when the countries that had the most tourists going to Greece entered into recession, Greece's income plumetted as well, and the debt just soared.
A little bit later, Greeks elected Syriza, which had simply accepted that they were in a debt spiral that would ultimately crush the country. Syriza's leaders told the other European governments that their debt had to be renegotiated (annoying for Greece's creditors, but at least it would be possible for them to pay in some capacity), or they'd leave the Euro-zone and just declare bankruptcy (thus they wouldn't pay back anything) (terrible for Greece, but perhaps not as terrible as the alternative).
The rest of Europe told them to fuck off for a variety of reasons (plenty of German newspapers had chosen Greece as their sacrificial lamb, often calling the people of Southern European countries lazy, the Spanish president back then wanted to crush Syriza because they had been associated with a growing Spanish opposition party, generally a lot of them were into fanatical fiscal conservatism).
Then Syriza chose not to leave the Euro-zone anyway (which provoked Varoufakis to leave the government, out of principle), and just stick to managing the country's misery. It has only been shit year after shit year for Greece since then, as any possibility of steering into a different direction was shot dead. It's just a country without hope at this point.