Alexis Tsipras, leader of the anti-austerity party Syriza, forms a coalition with the right-wing party Independent Greeks
Mr Tsipras vows to end Greece's "humiliation and pain" after Sunday's general election win
Syriza's victory raises fears about Greece's future in the euro as Syriza questions its 240bn euro bailout terms
European Commission chief Jean-Claude Juncker congratulates Mr Tsipras while reminding him of "fiscal responsibility"
Eurozone finance ministers met, with the fallout from the Greek election high on the agenda
All times in GMT
tweets, external: Congrats @atsipras #Syriza - I wish a speedy formation of a government that will be constructive both internally and with its EU partners
More from Jeroen Dijsselbloem, head of the eurozone finance ministers' group, who has said Greece must "stick to the rules". He told a Eurogroup meeting "there is very little support for a write-off in Europe". Syriza made renegotiating Greece's multi-billion euro bailout a central campaign pledge.
Image source, APReuters News editor Hugo Dixon says "a Grexit is closer, but still not the most likely" scenario. Speaking on the BBC News Channel, he said there was a 25% chance of a Greek exit from the euro by the end of this year. He said the new government could run out of money in March and without a Syriza policy U-turn there would be a risk of default, capital controls and even reintroduction of the drachma.
Syriza has a fully costed programme - something no Greek opposition party had in the past, says Costas Douzinas, a law professor at Birkbeck, University of London. It includes helping 300,000 poor families who lack food and heating. Speaking on the BBC News Channel, he said Greece's bailout conditions were "totally unviable - borrowing to pay off existing loans. Something has to give - but Greece's place in the euro is not threatened."
A.J. Darcy tweets, external: Fair enough, we in #Ireland made a mess of our economy, now we're paying back billions of Euro, somehow I can't see #Greece doing the same
tweets, external: Samaras opts for symbolism by opting not to be present for the handing over of PM responsibilities to Tsipras
The man on the left is Greek President Karolos Papoulias, listening to Mr Tsipras giving his oath. In a break with tradition, he took a secular oath, rather than the Greek Orthodox ceremony customary for Greek prime ministers.
Image source, AP
Image source, AFPGolden Dawn rally, 2014
How did far-right Golden Dawn manage to come third, with 6.3%, even though its leaders are in jail? It has built up a loyal following who like its anti-immigrant, anti-establishment rhetoric, experts say. Read our analysis here.
Stuart Knowles from Warrington emails: Whilst it is understandable that the Greek people want to see some respite from austerity, where do the leaders of this anti-austerity campaign think they will get the money to service their debts, and more importantly, when? I haven't seen any credible explanation of this, and to that end I am concerned for Greece's future. The issue stems from the reason they got into debt in the first place. If they don't have the means to pay off the money they owe now, then without significant reform, how will they ever?
It seems the leaders of this party want to test Europe's resolve when it comes to forcing them to leave the EU? I personally think it is extremely unfair to ask other countries to pick up the bill for your own mismanagement of affairs.
Toks tweets, external: Alexis Tsipras has his work cut out, the Greeks are fed up, if he doesn't deliver he will certainly not be treated kind. #greeceElections
The White House has said it is looking forward to working with the new Greek government. A statement read: "The Greek people have taken many difficult but important steps to lay the groundwork for economic recovery. As a longstanding friend and ally, the United States will continue to support their efforts and those of the international community to strengthen the foundation for Greece's long-term prosperity."
More pictures from Alexis Tsipras' swearing-in ceremony.
Image source, ReutersAlexis Tsipras, no tie, smiles after being sworn in as Greece's new prime minister.
Maria Petrakis, Bloomberg
tweets:, external Tsipras opted for civil oath to be sworn in, first time ever #interestingtimes
The swearing in ceremony is complete. Alexis Tsipras vowed to uphold the constitution and serve the Greek people. Greece now has a new prime minister.
Syriza leader Alexis Tsipras is being sworn in as the new Greek prime minister.
Mr Juncker has arrived for the meeting of eurozone finance ministers in Brussels.
Image source, EPAAndrew Walker, BBC News
The election campaign of the victorious Syriza party revolved around the idea of ending austerity and easing the debt burden.
It is not welcome to the country's bailout lenders, notably Germany. So we can expect the new Greek government to have difficult negotiations with the rest of the eurozone.
Neither side really wants Greece to leave, so a compromise seems likely, but an exit is nonetheless a possibility. Syriza's victory is also a boost for anti-austerity political movements in other countries struggling to reduce government borrowing.
Maria Petrakis, Bloomberg
tweets, external: Tsipras arrives to be sworn in. Not wearing a tie but looks dapper anyway
Greek economist Dimitri Mardas says the focus for Greece's new government and its eurozone partners will be restructuring Greece's enormous public debt. Take a look at his analysis of the future of the eurozone.