Image source, Getty Images

The Biden campaign has just sent out this statement, moments after Joe Biden was projected to become the first candidate in a quarter century to defeat an incumbent president:

"I am honoured and humbled by the trust the American people have placed in me and in Vice-President-elect Harris.

"In the face of unprecedented obstacles, a record number of Americans voted. Proving once again, that democracy beats deep in the heart of America.

"With the campaign over, it’s time to put the anger and the harsh rhetoric behind us and come together as a nation.

"It’s time for America to unite. And to heal.

"We are the United States of America. And there’s nothing we can’t do, if we do it together."

Laura Trevelyan
BBC World News America presenter

The atmosphere is jubilant here at BLM Plaza in Washington DC. People are singing, hugging, celebrating. "Donald Trump is gone, praise the Lord," shouts one woman.

"We won, hey hey hey, we won - nah nah nah nah, nah nah nah, hey hey, we won!" chant the crowd. People are taking selfies in front of the White House, the mood is ecstatic.

"Good trouble", one man’s t-shirt reads - a reference to the late congressman and civil rights leader John Lewis.

"How can we support Joe Biden when he supports abortion?" asks one man with a loud hailer. "Jesus wants us to think about that, folks."

But the crowd ignores him. There’s whooping, yelling, clapping - "Yeah, yeah, we did it!" people shout.

Image source, Getty Images

It took five marriage proposals before Jill Biden, a former English teacher from New Jersey, agreed to accept Joe's request.

She is his second wife, after his first wife and daughter died in a tragic car crash in 1972.

Mrs Biden, 69, has spent decades working as a teacher.

As well as a bachelor's degree, she has two master's degrees, and a doctorate of education from the University of Delaware in 2007.

Prior to moving to Washington, DC, she taught at a community college, at a public high school and at a psychiatric hospital for adolescents. She gave her address at the Democratic Party's convention this year from her old classroom at Delaware's Brandywine High School, where she taught English from 1991 to 1993.

While her husband served as vice-president, Mrs Biden was professor of English at Northern Virginia Community College.

"Teaching is not what I do. It's who I am," she tweeted in August.

Read more:

Jill Biden: From teacher to US first lady

Over the past few days, as vote-counting has continued, Donald Trump has made unsubstantiated claims of election "fraud" and vowed to go to the Supreme Court.

What he means is unclear. He and his campaign have filed lawsuits in a number of key states - including Michigan and Pennsylvania - calling for a stop to counting, but judges rejected them.

One challenge in Pennsylvania centres on the state's decision to count ballots that were postmarked by election day but arrived up to three days later. Republicans are seeking an appeal.

Matthew Weil, director of the Bipartisan Policy Research Center's elections project, told the BBC he was most concerned about this dispute as the nation's top court had been deadlocked on it before the election - and before Justice Amy Coney Barrett joined the bench.

"They did indicate in some of their dissents that they would be interested in taking it after. So I do think there is a risk that some of those [postal] ballots that were cast by election day and not received until Friday may be discarded. I think that would be the wrong result, but I think that is a legally possible result."

But Weil added that the election would have to be "very, very close for that to matter". We have projected the Biden win based on his lead in crucial Pennsylvania, where he is ahead by 30,000 votes.

You can read more about legal challenges here

Anthony Zurcher
BBC North America reporter

Joe Biden's projected victory after four days of painstaking vote-counting is the denouement of an extraordinary campaign, conducted during a devastating pandemic and widespread social unrest, and against a most unconventional of incumbents.

In his third try for the presidency, Mr Biden found a way to navigate the political obstacles and claim a win that, while perhaps narrow in the electoral college tally, is projected to surpass Mr Trump's overall national total by at least four million votes.

With his projected victory, Joe Biden becomes the oldest man ever elected to the White House. He brings with him the first woman vice-president, whose multi-ethnic heritage carries with it numerous other firsts.

Mr Biden can now begin the arduous task of planning the transition to his new administration. He will have just under three months to assemble a cabinet, determine policy priorities and prepare to govern a nation facing numerous crises and sharply divided along partisan lines.

Joe Biden has been dreaming of the White House for most of his 50 years in the public arena. With this prize of a lifetime, however, come the challenges of a lifetime.

By winning Pennsylvania, Joe Biden has won the vote to become the next president, pending any legal challenges.

Our projection of his win in the crucial state gave him 20 electoral college votes, bringing his total to 273 and surpassing the 270 needed to win the election.

Under the US system, voters in each state pick electors, who then gather a few weeks after the election to decide the winner.

Each elector equals one electoral vote, and the number of electoral votes per state is roughly in line with its population - so bigger states like Texas (38) and California (55) have more, while smaller states like Delaware (3) and Idaho (4) have fewer. In total there are 538 electoral votes, and a candidate needs 270 to win.

Pennsylvania was enough to get Biden over that halfway line. With leads in Georgia, Arizona and Nevada, he may well end up winning far more than needed - taking those three states would give him a total of 306.

Democratic challenger Joe Biden has won the US presidential election.

The BBC projects that he has reached 273 electoral college votes, meaning that he’ll become the president in January, pending the outcome of any legal challenges.

Pennsylvania has just been projected as a win for Biden.

And that's it, after a long wait, he is now over the threshold of the 270 electoral college votes needed.

Image source, Reuters

You might have noticed that some news organisations have already projected Arizona as a win for Joe Biden. The BBC still considers it too close to call.

The latest from the state, after new results came in from Maricopa County (home to the city of Phoenix):

• Biden is leading by 20,573 votes with 97% of ballots counted, according to the latest data. But his lead has decreased by more than 7,000 votes since the last update
• Trump supporters have been protesting in Phoenix, as ballot counting continues. Some carried pro-Trump banners as they chanted "four more years” on Friday and echoed the president's unsubstantiated claims of election fraud
• Arizona’s Secretary of State Katie Hobbs said in a tweet on Saturday: , external“My office has been putting out information for months about how election processes work in the state & all we do to ensure security & fairness. If you haven’t been paying attention, that’s on you, but don’t show up when you don’t like the result & scream fraud w/no evidence”
• We don’t know yet when we’ll have a clear result in the state

While much of our attention is on the presidential race, results from Congress are still trickling in. The House and Senate are the two national legislative bodies, and whichever party controls them can significantly affect how much a US president is able to achieve.

In their best version of election night, Democrats hoped to expand their majority in the House and take the Senate from Republicans (and, of course, win the White House).

That did not happen, and Democrats actually lost at least five seats in the House of Representatives.

CBS also projects that Democrats are still likely to lose several more races, including two in Florida, leaving them with a thin majority.

In the Senate, initial results appeared to show that Democrats had failed to gain the necessary four more seats to give them a majority.

But now two races in Georgia could change that.

On Friday it became clear that Republican Senator David Perdue had fallen short of the votes required to win re-election against his Democratic challenger Jon Ossoff. A candidate must get at least 50% to win.

It is now likely to go to a run-off vote in January.

The other race which will go to a run-off is between Republican Senator Kelly Loeffler and Democratic Raphael Warnock - who are vying to fill the seat of now-retired Republican Senator Johnny Isakson.

Two other races, in North Carolina and in Alaska, have not yet been called but Republicans are leading in both.

Read more about the winners and losers in the Congressional races.

Image source, Reuters

One of the most stressful jobs in the world right now has to be vote counter in the US election. Many are volunteers and have been processing votes around the clock since Tuesday.

With so much resting on the remaining thousands of ballots, there are reports that some workers have been threatened or intimidated:

• In Atlanta, Georgia, one election worker is in hiding after receiving threats, a local official said on Friday, reports CNN. A viral video showed him crumpling and throwing away a piece of paper, leading to false accusations of him throwing away a ballot. Around one million people have watched the video on social media - the paper that was crumpled and thrown away is a list of instructions that was placed into one of the envelopes, officials said
• In Arizona, police are providing protection for election staff, the secretary of state says. Protesters were "causing delay and disruption and preventing those employees from doing their job," she said
• In Phoenix, around 100 Trump supporters gathered at a Maricopa County election centre with military-style rifles and handguns (the law in Arizona allows people to openly carry guns)

• On Thursday, the Michigan attorney general tweeted, external, “please stop making harassing & threatening calls to my staff. They are kind, hardworking public servants just doing their job”

Image source, Reuters

Trump has tweeted to announce a “big press conference” in Philadelphia later today.

In an earlier tweet, which has since been deleted, he said the press conference would be held by lawyers.

The event is due to take place at 11:30 local time (16:30 GMT), so stay with us for more on that later.

We are expecting more results from Pennsylvania soon. That state alone is all Joe Biden needs to win the White House.

The Democrat is currently leading there by 28,833 votes.

Trump announced the press conference after writing a series of tweets making unsubstantiated allegations of illegality in the voting process in states like Pennsylvania. All four tweets were labelled as disputed and potentially misleading by Twitter.

The president and his team have launched legal challenges in several battleground states, some of which have already been dismissed.

You can read more on that here

Shayan Sardarizadeh
BBC anti-disinformation unit

More than 50 groups carrying the slogan "Stop the Steal" have popped up on Facebook in the last two days. The largest has drawn nearly 120,000 members.

The slogan is a reference to unsubstantiated claims by President Trump and some of his supporters that the election is being swung by "voter fraud".

One "Stop the Steal" group that attracted more than 360,000 members in a matter of hours was taken down by Facebook because of calls for violence.

Administrators of some of the new groups are warning their members to avoid using threatening or violent language.

Some have frequently changed their names, apparently in an attempt to avoid detection or removal by Facebook.

At least two "Stop the Steal" websites have also been created since election day to register volunteer activists, who are also trying to organise rallies in front of every US state capitol on Saturday.

Image source, Twitter

Things aren't going too well for Donald Trump on Twitter.

Four recent tweets have all been flagged as sharing content that could be disputed or misleading.

The Saturday morning tweets were in reference to what Trump claims were illegal votes that arrived after election day in states like Pennsylvania, erasing his lead. In fact, Joe Biden caught up in that and other crucial states due to the counting of legitimate ballots - many of them postal votes. This chain of events had been predicted by analysts ahead of the election.

Twitter has specific rules for world leaders, external, which means it will not ordinarily ban them for the same offences for which it would ban ordinary users. Twitter argues that such posts - even when violating its rules - are sufficiently newsworthy to stay up, with a handful of exceptions.

Instead, Twitter can label the posts of a world leader, hiding them from view and restricting engagement - but leaving the content viewable to anyone who clicks through a warning message.

It has repeatedly done this to Trump's tweets, leading to high-profile arguments with the president and his supporters.

Image source, Reuters

"Don't buy any green bananas," Pennsylvania's lieutenant governor John Fetterman (a Democrat) has just advised Donald Trump's campaign team on CNN.

He's suggesting that a decisive result could come very soon in the battleground state that would give Joe Biden the presidency if the votes break in his favour.

We've all been waiting many hours now for more results from the state. They are still counting in Allegheny County, which includes the city of Pittsburgh, and in Philadelphia. Both areas lean heavily Democratic.

Right now, Biden has a lead of 28,833 votes, having caught Donald Trump's lead of nearly 600,000 on Wednesday morning as more ballots were counted.

That's a 0.4% lead for the Democrat. We are expecting more results in the coming hours, which could push Biden over 0.5% - a margin of victory beyond which no mandatory recount is triggered.

Omar Sabir, the Philadelphia City Commissioner, and also a Democrat, just told CNN: "Be patient. This isn’t a microwave meal... There could be a war somewhere depending on the outcome of these results."

Things are moving so slowly in Pennsylvania because the state didn't start processing its postal ballots until election day. Ten times as many of these ballots were cast than usual - hence the delays.

Image source, Getty Images

Among the surprises of this US election was Kanye West joining the race. But how did the rapper do in his first presidential attempt?

Well, he's nowhere near power and has conceded after his self-styled "Birthday Party" collected just 60,000 votes out of an estimated total of 160 million cast.

West only appeared on the ballot in 12 states, missing the filing deadline in most others.

Another independent, Libertarian Jo Jorgensen, made a much stronger showing - claiming more than 1.5 million votes.

During her more conventional independent campaign, she made stops across the US to rally supporters, sought endorsements and pushed a platform guided by libertarian principles - small government and individual freedom.

Image source, Getty Images

But West's political career may not be over yet. He tweeted "Kanye 2024" this week, signalling another bid (perhaps timed with another album release?) may well be to come...

As the wait for a result continues, a clip of Democratic vice-presidential hopeful Kamala Harris doing an impression of her mother-in-law is recirculating on social media.

In the video, from last year, Harris talks about meeting Barbara Emhoff for the first time.

“She looks at me, puts my face in her hand… and she says, ‘Oh look at you. You’re prettier than you are on television. Mike, look at her!’” Harris recalls, imitating Emhoff’s accent.

The video racked up thousands of views and likes when it was re-shared on Twitter on Saturday.

Bit of light relief from the long wait?

Mike Wendling
BBC anti-disinformation unit

As Americans wake up, the president has continued to push his unsubstantiated claims that there is some sort of fraud going on in Pennsylvania’s vote count.

Courts have ruled that Pennsylvania can count ballots that arrive after election day, as long as they are postmarked on, or prior to, the day itself.

The president’s team did win a legal case to allow closer inspection of Pennsylvania counts. He hasn’t provided any evidence for his tweeted claim that “BAD THINGS” are happening during the vote tally.

The morning barrage is just the latest “fraud” claim by the president. As the BBC’s Reality Check team has reported, actual instances of voter fraud in the US are few and far between.

About half an hour after he posted the messages, Twitter put a warning label on them: “Some or all of the content shared in this Tweet is disputed and might be misleading about an election or other civic process.”

Our colleagues on the BBC's Visual Journalism team have produced this map, showing where either the Republicans (red arrows) or Democrats (blue arrows) have performed better than in 2016.

It's far from a consistent picture, with both parties gaining in some areas and losing support in others.

Unfortunately for the president, his gains are concentrated in states he already won last time around - for example strongholds such as Idaho and Utah.

Narrow gains in Trump states were enough for Biden to flip Wisconsin and Michigan for the Democrats. The blue arrows surrounding Atlanta, Georgia and Philadelphia, Pennsylvania, may yet be key to deciding the presidency.

See more maps and data from the election results.

The former prime minister of Denmark has dished out some advice to Donald Trump on how to leave office with "honour".

There is no indication that Trump - who has been making unsubstantiated claims of election fraud - will concede to Joe Biden, who is ahead in several of the few states still counting votes.

Lars Løkke Rasmussen tweeted a photo of himself leaving office after being defeated in the Danish general election last year.

Rasmussen's advice comes as Frank Bainimarama, Prime Minister of Fiji, congratulated Biden on his election success - even though ballots are still being tallied.

Slovenia's PM Janez Jansa took to Twitter on Wednesday to congratulate Trump for winning the election. Twitter put a warning on Jansa's tweet, saying: “Official sources may not have called the race when this was Tweeted.”

The race for the White House is coming down to who wins the few remaining battleground states - Georgia, Pennsylvania, Nevada, Arizona and North Carolina.

A win in just Pennsylvania or two of the other four remaining states would be enough to confirm Biden as president-elect.

Trump, meanwhile, needs to win Pennsylvania and three of the remaining four states.

A reminder of how this all works:

The president of the United States doesn't win by getting the most votes nationwide. Instead, candidates are trying to win the majority of electoral college votes.

These are essentially points assigned to each state, roughly based on the size of their population. In most states, the candidate who wins the popular vote is awarded all of that state's electoral college votes. As there are 538 in total, a count of 270 wins the presidency.

Now, with that in mind, here are the current results in the key states being closely watched as vote-counting continues.