The question debated for over 5 years that is like a recurring nightmare for the EU. If the country goes bankrupt or decides to leave the 19-nation Eurozone, the Greek debt crisis could create instability in the region and echo around the world.
Greek voters decisively rejected a deal of billions of euros in exchange for more cuts and austerity measures - but what happens next?
The next few days are crucial and German Chancellor Angela Merkel and French President Francois Hollande are desperate to keep Greece in the Eurozone as it could set a dangerous example for other countries that get into trouble.
On Tuesday, 7th July evening Eurozone leaders and finance ministers will hold an emergency summit as Greece wants to return to the negotiating table, believing a more favourable bailout deal could be reached in the next few days.
However, most of Europe's top politicians, such as Germany’s deputy chancellor, have already said it’s "barely conceivable" and that Greece has now "torn down the last bridges".
No country has ever left the euro currency but it’s now a real possibility - especially if creditors, such as the European Central Bank, refuse to resume talks.
With no new bailout agreed, Greece's banks could run out of money within days, with cash machines - currently rationed to €60 (£42) a day, now running dry.
Economists suggest it could then have to issue IOUs to pay pensions and public sector wages, or leave the euro altogether and return to the drachma to keep the economy afloat.
In one way, that could actually be good news as a new currency would probably see Greek exports become much cheaper.
Despite the ‘No Vote’, opinion polls still show more than 70% of Greeks want to keep the euro.
The economy has shrunk 25% since 2008 and it's been suggested the consequences of a euro exit could see a further 25% contraction.
The country’s massive tourist industry could be hit hard as travellers hide away from Greece and its surrounding islands, leading to more job losses.
One in four people in the country are already unemployed, and with under 25’s it’s nearly 52%.
A snowball effect from all the above could also see hyper-inflation, with everyday products rapidly increasing in value, and possibly mass demonstrations in the streets.
Chancellor George Osborne says there is no doubt a messy 'Grexit' would affect Britain, he wrote: "The Greek situation has an impact on the European economy, which has an impact on us. We cannot be immune from these developments.”
The FTSE-100 share index has lost 6% since the crisis began to escalate in late April, and shares in big UK companies could see significant falls.
The Greek tourist board and the Foreign Office are advising travellers not to rely solely on credit cards and cash machines.
They should carry three to five days' worth of euro notes and coins.
If Greece ditched the euro, Visa says business should continue as usual: "When a country exits a currency, we take steps to remove the old and add the new currency into our systems, meaning that the system for processing payments is still in place."