With 98% of the votes counted, 61.32% voted No, while 38.68% said Yes.
President of the eurogroup Jeroen Dijsselbloem is understandably not best pleased with the No vote. He said: "I take note of the outcome of the Greek referendum. This result is very regrettable for the future of Greece. For recovery of the Greek economy, difficult measures and reforms are inevitable. We will now wait for the initiatives of the Greek authorities. The Eurogroup will discuss the state of play on Tuesday 7 July."
John Cridland, the director general of the Confederation of British Industry, issued a statement, saying: "While the UK economy's direct exposure to Greece is minimal, we are not immune to wider Eurozone risks. We must now encourage all leaders, particularly those of the Troika, to act decisively to agree a deal, providing certainty for Greece and the wider Eurozone.
"Europe's policymakers should not hesitate to use every tool at their disposal to preserve growth and stability throughout the Eurozone."
Nigel Farage has had his say on the resounding No vote, praising Greek voters for "calling the EU's bluff". He added: "The EU project is now dying. It's fantastic to see the courage of the Greek people in the face of political and economic bullying from Brussels."
In a statement, the European Commission said that president Jean-Claude Juncker "is consulting tonight and tomorrow with the democratically elected leaders of the other 18 eurozone members [everyone except Greece] as well as with the heads of the EU institutions.
"He will have a conference call among the president of the Euro Summit, the President of the EuroGroup and the president of the European Central Bank on Monday morning [6 July].
"He intends to address the European Parliament in Strasbourg on Tuesday [7 July]."
Prime Minister Alexis Tsipras is addressing the nation: "You have made a generous choice. Greece has proved that democracy cannot be blackmailed; Greeks have made a brace choice, and one which will change the debate in Europe.
"I understand that voters have not given me a mandate against Europe, but a mandate for a sustainable solution.
"We are ready to continue negotiating with a reform plan, and the goal of restoring our banking system to normality quickly.
"I have asked the Greek president to convene the party leaders meeting tomorrow [6 Julty] for a briefing, but also hear their views.
"Today, we celebrate a victory of democracy, and tomorrow, together, we will continue a national effort to exit this crisis with a belief in the power of the people."
Looks like that's that. With 83.69% of votes counted and reported, No has a whopping 61.54% while Yes is on 38.46%.
Antonis Samaras, a former Prime Minister and the head of the opposition centre-right New Democracy party, has resigned following criticism of the way he ran the Yes campaign.
More good news for the No camp.
German Foreign Minister Frank-Walter Steinmeier: "We have now to accept such a result, it is the result of a referendum which the Greek people took part. What conclusions can be made is first and foremost a decision for Greece, therefore the ball is now in Athens' court."
This was the pollsters' last forecasts...
Metron Analysis : 'Yes' 48%, 'No' 52%
GPO : 'Yes' 48.5%, 'No' 51.5%
MARC : 'Yes' 48%, 'No' 52%
MRB : 'Yes' 46% to 51%, 'No' 49% to 54%
It's been another nightmare for the pollsters, who have all been way off with their forecasts.
Far from being a tight race, supporters of a No vote have won with a landslide.
With 70% counted, the No vote is maintaining a healthy 61.5%-38.5% lead. Turnout was just over 61%.
The Germans are really not happy with the No vote.
German Economy Minister Sigmar Gabriel told the Tagesspiegel daily: "With the rejection of the rules of the euro zone ... negotiations about a program worth billions are barely conceivable.
"[Alexis] Tsipras and his government are leading the Greek people on a path of bitter abandonment and hopelessness."
Gabriel, a member of the centre-left Social Democrat party - which partners Angela Merkel's Christian Democrats in government - added that Tsipras had "torn down the last bridges on which Greece and Europe could have moved towards a compromise".
A grey T-shirt-wearing Yanis Varoufakis, the Greek finance minister who threatened to resign if the country votes Yes, says that the Greek people have given a clear message.
"As of tomorrow, with this very generous 'No' that the Greek people have given us - ignoring the fear created with closed banks and by the media - we will try to co-operate with our partners and we will invite them one by one to see if we can find some common ground. And we will try to be positive.."
You really cannot beat this man's style...
The euro has fallen sharply on the back of Greece's resounding No vote.
It was down about 1.4% against the US dollar to $1.0955, and by 2.1% against the yen to ¥133.50.
French far-right leader Marine Le Pen welcomed the NO vote.
"This 'No' from the Greek people must pave the way for a healthy new approach," said Le Pen.
"European countries should take advantage of this event to gather around the negotiating table, take stock of the failure of the euro and austerity, and organise the dissolution of the single currency system, which is needed to get back to real growth, employment and debt reduction."
Greek analyst Yannis Koutsomitis says there was a huge generational difference in voting patterns, with 67% of the 18-33s saying No.
With half the votes counted, support for No is still holding firm with 61% of votes.
Some calming words from Italy.
Italy's foreign minister Paolo Gentiloni tweeted: "Now it is right to start trying for an agreement again. But there is no escape from the Greek labyrinth with a weak Europe that isn't growing."
Greek Labour Minister Panos Skourletis tells reporters: "The government now has a strong negotiating tool to bring about a deal which will open a new path for us."
The knives are out in the defeated opposition party
Hans Michelbach, of German Chancellor Angela Merkel's Bavarian Christian Social Union partners, told Reuters that Greece might be better off outside the eurozone.
"Now one has to ask the question whether Greece would not be better off outside the eurozone," said Michelbach. "Unfortunately, Greece has chosen a path of isolation," he said, adding that if a No vote won, as results indicate, he saw no basis for further aid for Greece.
Hundreds of jubilant anti-austerity No voters have started celebrating in Athens.
Capital restrictions at Greek banks will remain in place and savers will not be able to withdraw cash from safe deposit boxes, deputy finance minister Nadia Valavani told Alpha TV.
Deputy Finance Minister that, as part of those measures, the government and banks had agreed at the time that people would also not be allowed to withdraw cash from safe deposit boxes
A eurozone official has been quoted on Reuters as saying there was no emergency meeting of the Eurogroup - eurozone finance ministers - planned for 6 July, saying: "No way. [The ministers] would not know what to discuss."