Europe had been expecting Syriza to win this election but they thought they might win it narrowly, or need coalition partners, with all the compromises that that would involve but in fact they've won big.
The party has been given a very clear mandate and in fact they may even be able to govern on their own.
They will certainly have the ability, if they choose to use it, to make some very serious changes in Greece.
But there is a contradiction here at the heart of their policies, because they want to stay in the Euro and they want to keep their share of the single currency, yet they don't want to obey by the eurozone's rules on taxing, spending, budget deficits and they don't want to repay their debts.
The eurozone, effectively Germany, is going to have to decide - do we cut the Greeks loose, is the eurozone strong enough to lose a small member or do we make compromises and try to accommodate this new government, with the risk that they end up having to do the same with other countries.
Alexis Tsipras has spoken to huge crowds after his Syriza party won the Greek snap election.
Tsipras said that Greece was leaving austerity behind.
The outgoing Prime Minister Antonis Samaras says he respects the decision of the Greek people and says that his party, New Democracy, are willing to play a role as guarantor of European stability.
Greek Prime Minister Antonis Samaras has called Syriza leader Alexis Tsipras to congratulate him on winning the election, a Syriza spokesman has said.
Greece's far-left Syriza party will have 149-151 seats in the 300-seat parliament after winning a 36.5% share of the vote in the snap general election, according to the official projection.
The conservative New Democracy party is predicted to have come second with 27.7%.
There is a fundamental contradiction here, Syriza want to effectively break the Eurozone's rules by not repaying debt, by being let off various taxing, spending and budget deficit strictures as laid down by Berlin.
But at the same time they, and 75% of Greek voters, do not want to leave the Euro.
They believe they can square that circle by mediation but the German central bank is already saying that is not going to happen.
The problem for the Eurozone is that Spain, Italy, France all have anti-austerity parties as well. If they let the Greeks go their own way, everyone else will want to do the same.
Greece's anti-austerity leftist party Syriza could win an outright victory in Sunday's snap election, after commanding a 10 point lead over Prime Minister Antonis Samaras' conservatives, according to an updated exit poll.
Syriza was on track to take 36 and 38% of the national vote, well ahead of Samaras' center-right New Democracy party which was seen taking 26 to 28%, according to the updated poll.
The updated poll showed Syriza securing between 148 to 154 seats in the 300-seat parliament.
Further violence by Russian-backed separatists in Ukraine will lead to a "grave deterioration" in relations between the European Union and Moscow, Foreign Secretary Philip Hammond has warned.
Mr Hammond called on Russia to end its support for the separatists and exert its influence over the rebel leadership to bring an end to the attacks.
I am deeply concerned about the significant escalation in violence in east Ukraine over the past week. Recent announcements by the separatist leaders of further offensives, and their blatant refusal to abide by the ceasefire, raise serious questions about the commitments they made at Minsk.
I call on Russia to stop its material support to the separatists immediately, and use its considerable influence over the separatist leadership to stop these indiscriminate attacks, and fully abide by the commitments they made at Minsk.
Russia will be judged by its actions, not words. If the escalation in fighting continues, with tragic consequences for the local population, this will lead to a further grave deterioration in relations between the EU and Russia.
The Euro has fallen in early trading in Australasia after the Greek exit polls showed a probable victory for the far-left Syriza party.
The Euro fell nearly half a cent to around $1.1170, approaching an 11-year low.
A fresh gun battle erupted in Nigeria between militants and troops near the airport of the northeastern city of Maiduguri, a security source and nearby resident said Sunday evening.
"I can hear sporadic gun shots and bomb explosions, I am sure the boys are back to retaliate for what was done to them this morning," Bello Muhammad, who lives about 300 metres (yards) from the airport, told Reuters.
Suspected Boko Haram insurgents launched an attack on the outskirts of Maiduguri, including the airport that is used by military and civilian aircraft, on Sunday just after midnight but were repelled by the army in the early afternoon.