What we know:

— Angela Merkel's Christian Democrats lead as the strongest force in parliament, despite a severe dip compared to their 2013 haul. 

— Martin Schulz's Social Democrats slip to their worst election result in post-war Germany.

— The right-wing populist Alternative for Germany (AfD) wins its first seats in the federal parliament, also becoming the Bundestag's third power in the process. 

— The pro-business Free Democrats return to parliament, after missing the cut for the first time since the war last time around.

— The Greens and the Left hold station, scoring very similarly to four years ago. 

— No coalitions are practically viable without Merkel's CDU taking the lead. 

— The Social Democrats say they do not want to be in a coalition and intend to lead the opposition.

— Turnout will be higher than 2013's level of 71.5 percent, around 75 percent.

For a summary of the election results, click here.

All times in UTC/GMT (two hours behind local time in Germany).

01:01 That's it for our live updates. With 292 of 299 constituencies reporting, Chancellor Angela Merkel's Christian Democratic Union (CDU) and its Bavarian sister party the CSU have come out ahead in Germany's national election on Sunday, with a projected 33.3 percent of the vote.

23:33 It seems there's a delay in counting in Berlin, likely to cause much amusement among those familiar with the capital's not-so-German approach to deadlines. The Berliner Zeitung reports that final local results are coming in "unusually late" due to a "server problem." For now at least, the Berlin constituencies have no results on the election commission's homepage and they make up the majority of the 21 still outstanding. 

23:04 Final results should not be far away now, and in Bavaria, the vote count's finished. And it's a veritable mixed bag for the CSU. On the one hand, the Bavarian conservatives won just 38.8 percent of the "second" or party votes - that's a dip of 10.5 percent compared to 2013. However, in terms of the first-past-the-post race for seats, the CSU won all 46 on offer. Turnout was also markedly up, from 70.0 percent in 2013 to 78.2 percent on Sunday. The SPD seeks a case study for the definition of a "distant" second, scoring 15.3 percent in the Bavarian heartland. The AfD, on 12.4 percent, is hot on the SPD's heels. No wonder all the senior CSU politicians are echoing the Seehofer comment that the "right flank" of German politics is open. Party grandee Franz Josef  Strauss once famously said that there must be "no democratically legitimate party to the right of the CSU" in German politics. That appears to have changed.

22:44 French President Emmanuel Macron says on Twitter that "I have called Angela Merkel to congratulate her. We will determinedly pursue our essential cooperation for Europe and for our countries."

22:30 Economist and former Greek Finance Minister Yanis Varoufakis had more to do with the German government than he might have liked during his brief tenure in the Syriza government. His verdict on the vote is that "CDU, CSU & SPD reaped the harvest they had sown," prior to a plug for his Diem25 movement, seeking to unite centrist and progressive forces in Europe under a less diffuse banner than the traditional parties. 

22:25 On the subject of Twitter, naturally we have been keeping an eye out for the 45th POTUS, Donald Trump. Despite his own German background, the 140-character president has been busy with flags and national anthems for the most part on Sunday, plus a smattering of healthcare.

22:21 The EU's economic and financial affairs commissioner, Pierre Moscovici from France, has called the entry of the AfD into the Bundestag "a shock," saying that it "reveals doubts within the society." However, he adds: "German democracy is strong. No comparison with 1933." 

22:13 In pictures, the vanquished foes of Angela Merkel. This gallery focuses on all the others she's outlasted, although it seems we can add Martin Schulz to the list.

22:02 More news on prominent politicians' bids to win a seat directly in parliament. The German system is such that there are back doors to ensure the heavy hitters all make it to parliament. But still, it's a badge of honor to win a seat of your own, fair and square. The AfD's co-chair Frauke Petry has won her seat just to the south of Dresden in the east. The Greens' co-candidate Cem Özdemir narrowly missed out in the "Stuttgart I" constituency, falling 3 percent short of his Christian Democrat rival there. Social Democrat Foreign Minister Sigmar Gabriel claimed his spot in Salzgitter-Wolfenbüttel to the south of Hanover. 

21:54 And Karen Donfried, president of the German Marshall Fund, offered the US perspective on DW TV.

21:50 Some international reactions for you now, from our offices in Brussels and Moscow. Max Hofmann's just around the corner from the European Union, Emily Sherwin's in the Russian capital.

21:26 What connects the following things to the German election? Kenya, Jamaica, traffic lights, "black-red," and "red-red-green."

The answer is possible coalition constellations, named after the colors of the parties involved. As you may have noticed, some combinations allow for catchier nicknames than others. The one on everyone's lips right now is the "Jamaica coalition," but we can run you through the whole set in pictures here: 

21:22 At the SPD headquarters, on yet another bleak election evening for the party, is DW TV's Thomas Sparrow: 

21:10 As expected, the AfD's strength was rooted in the states that once made up Communist East Germany. According to Infratest dimap projections, the AfD was on course for around 21.6 percent of the vote in the former East. Four years ago, the AfD won 5.9 percent of the vote there. If confirmed, that would make the AfD the second-strongest party in that region, behind the CDU. The states, known in Germany as the "new federal states" since reunification, still score poorly by German standards in most economic indicators. It's perhaps also noteworthy that there was historically rather less migration into East Germany than West Germany.

20:50 And speaking of seats, Angela Merkel's spot in Mecklenburg-Western Pomerania is secure. In German, the constituency has the catchy name: "Vorpommern-Rügen/Vorpommern-Greifswald." With almost all counting stations returned, Merkel had 44 percent of the vote and an unassailable lead. However, she was 12 percent down on four years ago, a worse hit than her party looks set to take.

20:38 Finance Minister Wolfgang Schäuble has won his seat, one of the safest out there for the CDU, claiming 48.1 percent of the votes in Offenburg in southwestern Baden-Württemberg. Schäuble, the quintessential frugal Swabian (just ask Greece's Syriza government) and a major player in the CDU since before Merkel's political career even started, seems a shoo-in for another senior cabinet post. Aged 75 and confined to a wheelchair after an assassination attempt, Schäuble said before the vote that he intended to continue in top echelon politics for as long as his health permitted. However, some rumors are circulating that Schäuble might find a new senior post after the vote, potentially taking over as "president" of the Bundestag (the role of house speaker) from outgoing CDU veteran Norbert Lammert.

20:30 Interested in Christian Lindner and the FDP comeback? Then Simon Young's your man. And if your political heart bleeds green, Fabian von der Mark's been with Cem Özdemir, Katrin Göring-Eckardt and pals. We've paired these given that the two parties could well be forlornly seeking some common ground before long in coalition talks.

20:29 Over at the AfD, Charlotte Potts and Fanny Facsar are on duty as the populists celebrate their bronze medal. 

20:27 It's time to take you on a tour of the party headquarters, courtesy of our intrepid TV correspondents spending the evening with the politicians and supporters.

First up, Michaela Küfner reports from the CDU HQ: 

20:26 Monday trading is getting started in the far east, and the euro has dipped slightly (by 0.4 percent) against the dollar as the world's currency speculators seek to unpick the results. It's worth noting, however, that the euro has been gaining ground against the dollar pretty consistently since Donald Trump's election, climbing from near-parity to a value of $1.20, so there's some scope for the currency to take a hit.

20:09 DW's Michaela Küfner's clapped eyes on Chancellor Merkel now back at CDU party HQ. She warned of "tough weeks ahead" as the coalition talks get rolling. 

19:58 Reports trickling in from several major cities around Germany — Cologne, Hamburg, Munich, Leipzig, Frankfurt, Düsseldorf and Berlin — of impromptu protests in response to the AfD's success. 

Meanwhile, the Central Council of Jews in Germany called the surge in AfD support a major challenge for post-war Germany. 

"For the first time, a right-wing populist party with strong overlaps with the right-wing extremist scene ... has been voted into the Bundestag," the group said. "We expect our democratic forces to expose the true face of the AfD and lay bare its empty, populist promises." 

19:52 Marine Le Pen, leader of France's National Front (FN), and Geert Wilders, the leader of the Dutch far-right Party for Freedom (PVV) congratulated the AfD on its strong standing in the preliminary results.

Le Pen praised the AfD, saying the party was a "new symbol of reawakening of European peoples." In another tweet, Le Pen gave a personal shout out to the AfD's co-head Frauke Petry, saying Petry "led the party to this historic result." 

Wilders also tweeted his congratulations, posting a picture of himself alongside a smiling Le Pen and Petry, writing: "we will fight for our countries and our people. Always."

In another tweet, Wilders wrote: "The PVV number 2 in the Netherlands, FN number 2 in France, the [far right] FPÖ number 2 in Austria, AfD number 3 in Germany. The message is clear. We are no Islamic nations."

19:40 Before heading to Anne Will, the Greens' Cem Özdemir shared his initial feelings on Sunday's vote with DW's Fabian von der Mark. Asked about a coalition, he said: "If we see movement towards our direction, we are ready to take over responsibility. And if not, we are taking our seats in opposition." 

You can watch it in full below: 

19:31 There's a saying in German football, "nach dem Spiel ist vor dem Spiel." Literally, after the game is before the game. The moment it's full time, so the motto goes, it's time to prepare for the next one. In that spirit, the next high-profile politicians' round table begins on TV, hosted by star journalist Anne Will. This panel's perhaps not filled with elephants, but pretty sizeable political mammals: Defense Minister Ursula von der Leyen for the CDU, rising star Manuela Schwesig for the SPD, Greens' co-candidate Cem Özdemir, AfD co-candidate Alexander Gauland, FDP vice chairman Wolfgang Kubicki and journalist Hans-Ulrich Jörges. The Left party is notable in its absence.

19:15 The elephants' round closes with one final question to Angela Merkel, "will you be able to put a government together by Christmas?" 

The chancellor manages to promise nothing but simultaneously voice optimism, before going on to sum up her own style of politics in six words, saying "calmness is the seat of power." 

19:07 Jörg Meuthen claims the "that won't translate well" prize for the evening. He says it's nonsense to call the AfD anti-EU, but says the party does want to reform the bloc. The German he uses for the EU he envisages is an "Europa der Vaterlände." That translates as "a Europe of Fatherlands," and isn't liable to make a pretty picture as a headline. Though it does have a Nazi echo even in Germany, "Vaterland" is also a German word similar to the English idea of a "mother country" that long predated Hitler.

19:02 Back in the studio, the talk is turning to the ideological differences between the two probable "kingmakers," the FDP and the Greens. Christian Lindner of the FDP fires the first salvo, saying he could not support all current plans promoting (often subsidizing) renewables. The Greens' Katrin Göring-Eckardt agrees that any talks will be "hard" and "complicated." As well as these policy difficulties, Merkel will also have to walk a ministerial tightrope: Which cabinet posts will satisfy the two junior partners, while also retaining important posts for her CDU stars and for the CSU's Bavarians?

18:57 An update from outside the ARD TV studios that are gripping much of Germany at the moment. Protesters in Berlin, which typically leans to the left in its voting habits, have taken to the streets, upset at the AfD's showing. 

Read more:  Anti-AfD protests break out in Berlin after German election

18:54 Fiery AfD-related exchanges continue in the elephants' round — the Left's Katja Kipping is first to directly allude to wartime Germany, saying "I would like to see nobody vote for Nazis." Meuthen's one-word response is "outrageous." The AfD argues that they're portrayed as more right-wing than they are.

18:47 Still not up to speed on the Alternative for Germany? We've got your back: 

Read more:  AfD: What you need to know about Germany's far-right party

18:44 Meuthen also said that it was unfair to claim the AfD represented far-right views, which didn't cut the mustard with the panel. The Left party's Katja Kipping cited the example of Alexander Gauland saying Germany could be proud of its World War II soldiers, while Merkel brought up a call - again from Gauland - that an SPD politician with Turkish roots should be "entsorgt" (literally "disposed of," it's what Germans do with garbage that can't be recycled) back in Turkey. 

18:38 The AfD haven't sent either of their "top candidates," Alice Weidel or Alexander Gauland, to the Elefantenrunde, dispatching party co-chair Jörg Meuthen instead. Challenged on the far-right comments from some members of the party, he says that it's the duty of parliament to offer an agenda in the interest of the German people, before stressing that this "most certainly" includes millions of German citizens and inhabitants with roots overseas. Meuthen goes on to say that dissatisfaction with the government is often highest among people with a migratory background.

18:33 Schulz and Merkel continue trading blows. Schulz reiterates that "this government has been un-elected, and you, chancellor, are the biggest loser." That claim is half true. Merkel's lost the most ground this time, according to partial results. But Schulz and the SPD have hit a deeper bottom.

18:30 Merkel seeks the high road in response, saying she finds it "sad" that the coalition's work was summed up so negatively by Schulz. Schulz tries to interject and Merkel pulls him up asking if she can finish her sentence. That's the closest to boiling point you're likely to see Germany's sub-zero chancellor on stage.

18:26 The SPD's Schulz asked if he's really unwilling for any coalition talks: "A strong opposition, in the phase in which we're in, is really important," Schulz says, saying the SPD will be a strong opposition for a coalition between the CDU/CSU, FDP and Greens. Schulz tries to argue that the necessary concessions will not pose an ideological problem for Merkel, hinting that they would offend his political self more. Merkel's grin is clear for all to see, as the camera crew keep cutting to her. Schulz also said that if the result shows anything, it's that the "grand coalition has been voted out." Mathematically, that's not quite true, but he's alluding to the big losses suffered by each party in the outgoing coalition. 

18:21 Merkel says that she had "wished for a better result," with party allies hinting before the vote that the target was to be at or around 40 percent. However, the chancellor is quick to add that "we are clearly the strongest party."

18:19 It's time for the TV highlight of election night in Germany, the so-called "elephants' round table" ("Elefantenrunde"). Despite the name, there are no megafauna involved. This gathers top candidates from every party set to get seats in parliament, including Angela Merkel and Martin Schulz, to talk about the results, possible coaltions, and what Sunday's vote will actually mean for the next four years of government.

18:10 Greens' Cem Özdemir says that a clear climate change road map would be a precondition for his party in coalition talks. That could prove a sticking point not only on renewables, but on Germany's heavy use of coal to cover the nuclear phase-out.

18:05 Polling institute Infratest dimap found that 60 percent of AfD voters said they chose the party because they were dissatisfied with the others, rather than being convinced in the AfD's policies. This figure was far higher for the AfD than rival parties.

17:59 Here's some video footage from Angela Merkel's first speech after the polls closed: 

17:52 The FDP's Christian Lindner, asked about a three-way coalition on ARD, warned of severe FDP differences with both Merkel's CDU and the ecologist Greens, saying "let's keep the ball low," a German idiom that roughly amounts to "let's wait and see."

17:43 One of the AfD's top candidates Alice Weidel told DW's Charlotte Potts more about her party's promise to launch an inquiry into "where Angela Merkel has broken the law." She said the inquiry will particularly focus on the chancellor's refugee policies.

"The refugee policy has no legal basis," she said, noting that it wasn't put up for a vote in German parliament before being put into place. "It is undermining the system of parliament."

Read more:  Bundestag questions legality of Angela Merkel's refugee policy

"We have to scrutinize the executive. This is why we have been elected into parliament now," Weidel said.

17:25 The Left party's Sahra Wagenknecht told ARD television she was happy with her party's second-best results ever. Asked about the AfD she said that, in opposition, they would not address social issues. The two parties are almost certain to be in opposition together, and Wagenknecht said that she "won't give them the pleasure of sweeping villifcation." Some have argued that parties' and the media's criticism of the AfD might have been counterproductive, not to mention adding to the party's profile. Horst Seehofer of the CSU made similar comments, saying the AfD had been "overhyped." 

17:20 DW's Kathleen Schuster is in Cologne for a planned anti-AfD election-evening rally. Protest banners include slogans like "nationalism is no alternative," and "whoever stays silent supports it." 

And, meanwhile, in Berlin, Kate Brady's on hand for a similar demo. 

17:17 Unusually, at a time when talk is usually all about a coalition, it's the role of opposition leader getting a lot of the domestic attention. It seems that the Social Democrats are positioning themselves for this role, quite possibly a response to the results. Should the SPD enter into another grand coalition after all, that would leave the AfD leading the opposition in the Bundestag. Here's more on the parliamentary opposition's role and importance in Germany: 

Read more:  What is the role of Germany's parliamentary opposition?

17:15 Over at the Greens, DW's Fabian von der Mark witnessed supporters first cheer their result, only to then boo news that the AfD was on track to beat them by around four percent. 

17:05 The Bavarian state premier, Horst Seehofer of the CSU, has lamented a "vacuum on the right flank" in the current vote, saying that the conservatives would have to close this again, by ensuring that "Germany remains Germany." He said that keeping a grip on immigration would be the best protection against the far-right. The CSU also struggled, even in conservative bastion Bavaria, racking up its worst result since the 1949 elections. However, that still constituted 38.5 percent in Bavaria, six points more than the national average for the Christian Democrat CDU/CSU alliance.

17:03 Here are video highlights from Schulz's speech to supporters in Berlin a few minutes ago: 

16:58 If the SPD really does want to lead the opposition for four years, that could put Merkel into talks with the ecologist Greens and the pro-business FDP. One major sticking point is likely to be climate and energy policy. The Greens favor more subsidies and efforts to advance renewable energy usage, while the FDP argues that current efforts are inefficient and that competition and innovation are more likely to provide solutions. Read this detailed wrap of the difficulties of setting up what's known as the "Jamaica coalition." 

German election: Can the Greens and FDP join Angela Merkel in a coalition?

16:54 Merkel said that the AfD posed a "challenge" for her government, and she was planning to win back the voters who flocked there by better addressing their concerns and problems.

16:52 Merkel says that, considering the 12 years of government led by the CDU/CSU, it was "absolutely not guaranteed" that they would be returned as the strongest force in parliament.

16:51 Angela Merkel's first response since the polls closed. "We have the right to try to form a government, and no government can be formed without us," she says, keeping all her theoretical coalition options open. However, given comments from the SPD, Merkel looks set for talks with the FDP and the Greens about what could prove an uneasy alliance. 

16:49 The Greens' co-candidate Cem Özdemir says his "joy at our results is mixed with sorrow," because of the other results: "We live in a republic that has changed. Nazis are returning to the Bundestag," Özdemir says, presumably in reference to the AfD.

16:42 More from the FDP's Christian Lindner, talking to ARD television. The pro-business politician said that there would once again be a "group for freedom" in parliament. In 2013, for the first time since the war, the FDP failed to make it into federal parliament, and Lindner appealed on ARD for this first to also be a last.

16:38 The Free Democrats' Christian Lindner kept it short and sweet on Twitter in response. "Just one word: thanks."

16:36 Schulz called his party  a "bulwark for democracy" in Germany. He went on to say that the Social Democrats intend to go into opposition in the next government, reinforcing the initial comments from Manuela Schwesig.

16:35 Martin Schulz: "Especially depressing for us today is the strength of the AfD," the SPD candidate says, calling the result and the return of a far-right party to the Bundestag a "caesura" for German politics and one that "no democrat can accept." 

16:31 "Today is a difficult and a bitter day for the Social Democrats. I don't want to beat about the bush. We missed our targets and lost the election," Schulz says, before thanking supporters and party members for their efforts. "We clearly didn't manage to keep and expand on our traditional voter base."

16:31 SPD chancellor candidate Martin Schulz is about to give his first reaction. 

16:24 The Free Democrats, headed up by Christian Lindner, appear to be the other big winners of the evening. Party general secretary Nicola Beer told ZDF television that it wasn't yet clear whether they'd seek a coalition with Merkel. "For now, we will wait and see," she said.

16:15 AfD party members celebrated as they watched the first exit polls come in, reports DW's Charlotte Potts. The far-right party met in a Berlin nightclub to watch the results.

16:11 One of the Alternative for Germany's top candidates, Alexander Gauland, said on Sunday that Angela Merkel "should wrap up warm, we'll hound her" in opposition. Dozens of AfD MPs will be on their way to the federal Bundestag for the first time, at the second attempt for the party. In 2013, they fell just short of the five-percent hurdle. Gauland also said, in words more than a little reminiscent of Donald Trump, that "we will get our country and our people back." 

16:09 Deputy Social Democrat party leader Manuela Schwesig, on German broadcaster ZDF, has said her party intends to go into the opposition. Prior to the vote, most German analysts believed the SPD would only want another four years of "grand coalition" government if they maintained around 24 or 25 percent support, to ensure that they were influential enough in coalition with Merkel. This could force Merkel to seek an alliance with both the Greens and the Free Democrats.

16:03 If they prove accurate, these projected results would constitute a major blow to Germany's two largest parties. Both have lost millions of votes compared with their 2013 tallies. For the SPD it would be the worst election result in post-war history, while the Christian Democrats only ever fared worse once, in the very first post-war elections of 1949.

16:00 Polls close across Germany. The first official exit polls, usually a reliable indicator of the final results, suggest a 12.5-point lead over the competition for Angela Merkel's Christian Democrats. But under Germany's parliamentary system, that won't suffice for the CDU/CSU to govern alone. However, Sunday's results give Merkel more theoretical options than she had last time around.

15:45 Roughly 61.5 million Germans were eligible to vote in Sunday's elections. Based on partial counts during polling day, a similar proportion looks to have done so as in 2013, when 71.5 percent took part.