Angela Merkel tells supporters: "We have mandate to govern"
Martin Schulz's centre-left SPD comes a poor second
The SPD rules out another 'grand coalition' with Merkel's CDU
Right-wing nationalist AfD is set to come third
AfD has never been in parliament before
Liberal FDP heads for a return to the Bundestag
And this is the moment Germany's exit polls came in: applause from Merkel supporters, louder cheers among AfD followers...
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Germany election: The moment the exit polls came in
People have taken to the streets in Germany's financial capital to protest against the right-wing nationalists' success.
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The French right-winger congratulates her allies in the AfD for their "historic" achievement.
"It is a new symbol of the revival of the European peoples," the National Front leader adds.
And here's the latest poll results from ARD/Infratest.
The BBC's Maria Byrne tweets that the crowd is getting noisier outside the AfD's headquarters in Berlin.
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Image source, OtherSo, Angela Merkel has been re-elected for a fourth term, although she admitted she had hoped for a "better result".
She has led Germany since 2005, enduring a global financial crisis, turmoil over migration policy, and the disruption caused by Brexit.
So, who is Mrs Merkel? Here's our profile with archive pictures and analysis.
Angela Merkel makes it clear again that there are two arithmetic possibilities for a new government for Germany - despite the SPD having ruled out taking part.
While she had noted the SPD's position, "perhaps we can talk again tomorrow," Mrs Merkel says. (See 6:37pm entry).
The SPD's Martin Schulz tells the FDP and the Greens that they needn't worry, as "Mrs Merkel will give them anything to stay in the chancellery".
"I know how these coalition talks go", he adds.
Taking part in the "elephant round" TV debate, Green candidate Katrin Göring-Eckardt says the priorities for her party include Europe and climate change.
The FDP's Christian Lindner says his party is "not condemned to govern", but adds that the party has a responsibility.
He again criticises the SDP for ruling out being part of a coalition.
Political leaders, including Mrs Merkel and Mr Schulz, are taking part in a so-called "elephant round" discussion, which is broadcast live on German TV.
Antifascist demonstrators in Cologne have lit flares as they take to the streets to protest against the AfD, according to Germany's tabloid Bild.
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Beatrix van Storch, one of the AfD's leaders, tells the BBC that Sunday's election result is "a huge success and it will change the political system in Germany, and it will give back a voice to the opposition".
Ms van Storch says her party will "give the people who have not been represented in the last parliament a voice again".
"We will start debates on migration, we will start debates on Islam, we will start debates on ever closer union."
Demonstrators angry at the AfD's electoral success have gathered in Berlin this evening
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Image source, ReutersWe have already told you about a protest against AfD at Alexanderplatz in Berlin. Now some trouble has broken out.
Police say bottles have been thrown at officers:
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And just to make clear what a dramatic development AfD's rise on the national stage is, Germany's Central Council of Jews has issued a dramatic warning.
Germany is facing its biggest challenge since 1949, it says,
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The projections used by both major broadcasters give AfD over 13% of the vote:
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AfD co-leader Alexander Gauland, speaking after the projected results showed his party in third place, said they would "hunt down" Mrs Merkel or whoever formed the next government.
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Quote MessageWe will take back our country and our people.
Alexander Gauland, AfD
"We are very far from each other in many areas," says senior Green (and premier of Baden-Württemberg) Winfried Kretschmann, regarding the differences between his party and potential coalition partners in the CDU/CSU and FDP.
But someone has to govern, he adds.
Jenny Hill
BBC Berlin correspondent
This is a disastrous night for Mrs Merkel. She's managed to win but this is her worst-ever election result.
What we're seeing here is Mrs Merkel being punished for opening Germany's door to hundreds of thousands of migrants. Mrs Merkel's campaign team saw this coming very late.
She urged voters to mobilise. Perhaps what we're seeing is that didn't happen.