In the run-up to the creation of the EMU, Greece apparently cooked its books completely. It claimed to have met the Maastricht criteria - with government deficits no more than 3% of GDP, amongst other criteria - and the EU believed the Greek statistical office.
More here and here. And this in German, but behind the FAZ paywall...
Recent "revisions" show that this was not the case, and indeed Greece met the Maastricht criteria for only a single year, instead of permanently reducing its government spending, measured as a percentage of GDP.
The specific sins of Greece: public hospitals were so severely in debt that the revision of their debt made up a full percentage of GDP; government finances were not reported correctly because revenue shortfalls, higher social costs and much higher government wages were not reported; government corporations were assumed to have much larger operating funds; military expenditures were falsely reported; one-time payments were booked as recurring revenues; swaps were depreciated incorrectly; government interest rate payments were booked incorrectly; state guarantees for loans were not booked correctly; government pension reserves were valued well above their value; regional and local government debt was ignored; non-budget government spending was not included; EU transfer payments were incorrectly reported; and, to top everything, the inability to check individual entries for single item bookings.
This is, bluntly, fraud: Greece defrauded its way into the EMU. They lied - and apparently the statistical office was complacent, compromised and unable to speak truth to power - and weaseled their way into the dreamland of EMU subsidies and support. They trade a pathetically weak currency for the Euro. That comedy of errors, omissions and the like
What will happen?
Nothing. A few heads might roll (meaning that they'll retire with pensions), but nothing serious will happen to Greece for this fraud.
The only real effect that this will have is that no one will trust Greece to do anything other than lie when asked about statistics.
The consequences? None. The EMU cannot afford to have Greece unceremoniously tossed out on its ear (which it so richly deserves: Greece in its current form lives off the EU and is an active drag), and pure formally the EMU has no process to do such a thing.
Hence: business as usual, the Greeks will slowly let the statistics show the true misery of that parasite economy, as it will ensure EU subsidies to get government spending there under control. Can't have the Greeks actually have to be miserable for the complete and total failure of any of their administrations to get this sort of corruption and incompetence under control.
Hence the EU taxpayer, that beast of infinite burden, will pay for Greece's fraud and lies. About par for the EU, that. Never find and punish the guilty when fraud, incompetence and outright corruption makes up the basis for political life. That gets it all too close to home...