Image source, Reuters

To our readers who are just joining us, good morning and welcome to our live coverage of the US election.

Our main news is that Joe Biden has delivered his first speech as president-elect in Wilmington, Delaware. He shared the stage with his VP Kamala Harris, who is making history as the first woman - and first person of colour - in the role.

Biden said it was "time to heal" the US, and appealed to people who voted against him: "Let's give each other a chance."

"I pledge to be a president who seeks not to divide, but to unify; who doesn't see red states and blue states, only sees the United States," he said.

He also said that he would form a Covid response committee and make sure it's ready to implement decisions from his inauguration day in January. Both Biden and Harris came on stage wearing masks.

Meanwhile, Harris acknowledged her historic election, telling the crowd: "While I may be the first woman in this office, I will not be the last."

We have more here about what they had to say.

Nick Bryant
BBC New York Correspondent

Image source, Getty Images

Donald Trump has become one of only four incumbents in the modern era not to be re-elected for a second term, and the first president to lose the popular vote in consecutive elections.

So what happened?

Trump won the presidency in 2016 partly because he was a norm-busting political outsider who was prepared to say what had previously been unsayable.

But Trump also lost the presidency in 2020 partly because he was a norm-busting political outsider who was prepared to say what had previously been unsayable.

Then there was what critics derided as his creeping authoritarianism, seen after the election in his refusal to accept the result.

And a political problem for Trump was that he failed to expand his support beyond his core Trump base. Nor did he try hard to do so.

Read the full story here

Image source, Reuters

Since Biden was announced as the election winner, messages from world leaders have poured in - most of them positive. Here's what some of them have had to say.

• Boris Johnson, UK, said the US "is our most important ally and I look forward to working closely together on our shared priorities, from climate change to trade and security"
• Narendra Modi, India, called it a "spectacular victory", and added effusive congratulations to Kamala Harris, who is half Indian: "Your success is pathbreaking, and a matter of immense pride not just for your chittis, but also for all Indian-Americans"
• Angela Merkel, Germany, said that "our transatlantic friendship is indispensable if we are to deal with the major challenges of our times"
• Nicolás Maduro, Venezuela, said his country "will always be ready for dialogue and understanding with the people and government of the US"
• But Ayatollah Ali Khamenei, Iran, said the election was "a spectacle", adding: "This is an example of the ugly face of liberal democracy in the US. Regardless of the outcome, one thing is absolutely clear, the definite political, civil, & moral decline of the US regime"
• And Alexander Lukashenko, Belarus - whose own election, widely viewed as rigged, sparked nationwide unrest - condemned the US election result as "a travesty of democracy"

Read more world leaders' reactions.

Ritu Prasad
BBC News writer, Florida

We've been asking our readers for their most pressing questions about the US election. Now it's our turn to respond.

Stéphane Longuet, 50, from London asks: Is it possible electors would designate another winner? Could some electors from Pennsylvania decide to vote for Donald Trump instead of Joe Biden or are they legally bound to follow the popular vote?

This is a great question - so let's dive into what the deal is with these so-called "faithless electors".

The majority of states in the US, including this year's key battlegrounds of Arizona and Michigan, have laws that bind electors to vote for their state's majorities.

This year, the Supreme Court unanimously upheld those laws, saying electors have "no ground for reversing" the popular vote in their state, noting that in America, "We, the People rule".

Of course, this doesn't mean that we haven't seen faithless electors before, though it is rare.

In 2016, ten electors reneged on their popular vote winner to vote for other candidates. And way back in 1796, one elector switched to vote to the opposing party.

But it's important to remember these faithless electors have never actually changed the outcome of a presidential election.

According to FairVote, an election reform nonprofit, across 58 presidential elections with more than 23,500 votes cast, only 90 electors have failed to honour the popular vote.

Now a quick look at Pennsylvania: the state doesn't require electors to vote in line with the popular result or penalise faithless electors. However, any swaps here are unlikely, as the party campaigns choose their electors in the state.

Click here to learn more about this project - or submit a question of your own.

When votes were still being counted, and Trump's lead was narrowing, a number of Republicans came out in support of the president and his allegations - presented without any evidence - of ballot irregularities.

Since Biden was declared the winner, however, most of these supporters have been conspicuously silent.

Just a few have continued to voice their support for Trump. One is Marco Rubio, who said the issue of voter fraud should be examined in the courts.

Missouri Senator Josh Hawley also tweeted, saying the winner shouldn't have been declared until the votes were able to be counted and recounted.

Senator Lindsey Graham also repeatedly backed Trump, and even donated $500,000 towards the barrage of lawsuits the president has launched in battleground states.

However, he has not commented since Biden's win was confirmed.

Shrai Popat and Holly Honderich
BBC News, Washington DC

Repairing the divisions in America has been an animating theme of Biden's candidacy.

He has vowed to be a president for all Americans, to restore the "soul of America" and fix the national discord he blames on Trump.

It might be a tough sell for some 70 million Americans who cast their ballot for Trump this year - roughly eight million more than sent him to the White House in 2016.

But for those we saw gathered outside the White House on Saturday, it's a welcome message.

We asked those celebrating how they would speak about President-elect Joe Biden’s victory with those who support Donald Trump.

Some tried to foresee how conversations with family members might look like in the coming days. "I think I'm going to say Biden is the president for everybody, you just don’t know it yet," Anisley Valdes told us.

Many of her immediate family members are based in Miami, Florida, and are lamenting Trump’s loss.

For Ken Wright, 55, a lifelong Republican who only switched his party affiliation in January, the keyword is "compromise'.

Others were less immediately empathetic. Luke Rosansky said: "It’s time to put this racist agenda behind us."

Biden reached out across the divide in his speech, saying he wanted to be a president for the whole nation.

He said he understood the disappointment of Trump supporters, but said: "Let's give each other a chance."

We asked two Republicans from our voter panel what this moment means for them.

It's so exhausting because Trump has been fighting his entire presidency. People never left him alone to let him do his job.

I'm exhausted, I'm so tired of it. I've had to turn off social media and unplug and calm myself not to stress about it. I don't believe in the results, Biden can't legally become president yet. I believe that everything will be settled in the Supreme Court.

If Biden does win, it's going to be a crappy next four years. It will inspire me to get involved more for the next election with the Republicans in my town.

The mainstream media has jumped the gun projecting that Biden will win the electoral college.

Nothing has changed since yesterday and President Trump's campaign has signalled that he will mount vigorous legal action in multiple swing states on Monday.

The American political process continues and this is the media playing psychological warfare to make President Trump seem like a sore loser in the court of public opinion.

These are members of our US election voter panel. You'll hear more from them throughout the week.

Join the conversation:

• We want to hear from you - what questions do you have about the US election?

The Trump campaign hasn't lost hope yet, according to reports from our sister network CBS News.

A senior campaign official told CBS they knew from the start this would be a drawn-out election fight. They said as long as there was a path forward, there is hope for four more years.

When asked about whether they felt the president's legal challenges in several key states would be successful, the official said anything can happen - and Trump has pulled off "crazier stuff before".

The official added that no one at the campaign headquarters was surprised by the media projecting it for Biden. They're ready to fight, and have already been sorting through Trump's "voter fraud" hotline.

Image source, EPA

While some world leaders have offered their congratulations to the US president-elect Joe Biden, one is being more cautious.

Mexican President Andres Manuel Lopez Obrador, who is known as Amlo, says it's too soon - and that he wants to wait for "all legal issues" to be resolved, referring to lawsuits filed by the Trump team, alleging irregularities in vote counting. Trump has not presented evidence for these claims.

"We don't want to be imprudent," Amlo told reporters earlier on Saturday.

"We don't want to act lightly and we want to respect people's self-determination and rights."

Anthony Zurcher
BBC North America reporter

In an earlier time, Joe Biden’s victory speech would have seemed fairly routine.

The president-elect spoke of unity, of ending acrimony, of the potential and power of the American people. Those are sentiments many a winning politician has touched on in the past.

Coming on the heels of Donald Trump's tenure, though, they mark a sharp contrast. The president Biden will replace is one who is often criticised for stoking cultural divisions and doing little to tamp down the unrest that broke out in many US cities earlier this year.

Biden spoke of his election being an "inflection point", that would allow the American people to make a decision about "who we are and who we want to be".

As Saturday night’s speech showed, at the very least, the Biden presidency will mark a change in rhetoric.

The American people have a president-elect who talks about bringing the country together; about being a leader for all the people. But saying it is the easy part; now he has to do it.

Ritu Prasad
BBC News writer, Florida

We've been asking our readers for their most pressing questions about the US election. Now it's our turn to respond.

Colin, 78, from Keighley, UK, asks: Why were there more postal votes for Biden?

Let's take a look back at the months preceding Election Day. You may recall Trump early on frequently discouraged the use of postal voting, alleging without evidence that there was widespread fraud.

Though the president's campaign later told supporters voting by mail was fine, many chose to instead turn out to the polls.

This is why analysts correctly predicted we'd see an initial lead for Trump - because many votes cast in-person were from Republicans. In-person votes are counted first.

On the other hand, Biden supported postal voting in the pandemic from the start, so, in turn, more Democrats opted for this method.

And as more of the postal votes sent in were counted (which is all legal), Biden saw his vote count rise.

Click here to learn more about this project - or submit a question of your own.

Joe Biden may have just appeared in Delaware to declare his victory in the election, addressing those who voted for Donald Trump saying: "I understand your disappointment" - but backers of the president are not quite prepared to accept the Democrat.

The BBC's Jane O'Brien spoke to Trump supporters gathering at the Washington Monument today.

"I think there's a tremendous amount of fraud," one supporter said, when asked whether she would accept the results. "There was no way some of those numbers could have gone up in the time frame they did."

Trump has claimed that there were irregularities in the election. Though election officials have said there is no evidence of this, some of his voters are convinced.

Watch the full clip below.

Dharshini David
Economics Correspondent

When the celebrations - and the challenges - are over, the 46th president of the United States will face an unenviable task: how to nurse his economy back to full health in the face of an ongoing crisis.

The coronavirus pandemic has prompted the number of people out of work to soar and while employment has been creeping back up, it remains 10 million below pre-crisis levels. And the existing government support package is lapsing.

With restrictions holding back consumer spending, which accounts for two-thirds of the US economy, the pressure is on for Joe Biden to pass a fresh, generous package quickly. He pledged in his campaign that he would prioritise the livelihoods of Americans as president. As part of that, he has talked about expediting support to businesses that have managed to keep workers on payroll and boosting unemployment benefits. He’s also keen to pour money into infrastructure.

But the real challenge will be getting these plans past a potentially divided Congress. And with interest rates already at rock-bottom, the burden of propelling the recovery will fall to the White House.

Economic growth has, on average since World War Two, fared better under Democratic presidents than Republican ones. But even if he manages to get a stimulus package through Congress, Biden may find it a challenge to match that record while the pandemic has the upper hand.

Earlier today, India's Prime Minister Narendra Modi offered his congratulations to Joe Biden on Twitter for his "spectacular victory".

And to Kamala Harris, whose mother was Indian, he wrote: "Your success is pathbreaking, and a matter of immense pride not just for your chittis [aunties], but also for all Indian-Americans."

Modi's friendship with Trump was well covered, but it remains to be seen what a Biden-Harris administration will do for the US-India relationship.

As our correspondent Rajini Vaidyanathan in Delhi notes: "India has long been an important partner to the US - and the overall direction of travel is unlikely to change under a Biden presidency."

Read more:

• Kamala, Kashmir and Modi's friend all on ballot in US election

• The many identities of the first woman vice-president
• Why Kamala Harris embraces her biracial roots
• What Biden's victory means for rest of world

Anthony Zurcher
BBC North America reporter

Kamala Harris’ brief speech focused heavily on the historic nature of her election as the first woman vice-president.

“While I may be the first woman in this office, I will not be the last,” she said, adding that her election sends a message to girls and women around the country - that it is possible to put someone who looks like them in the White House.

For many Democrats, this is one of the most exciting aspects of Biden-Harris ticket.

Four years after Hillary Clinton put “18 million cracks in the highest glass ceiling” but ultimately fell short of the prize, this is a measure of redemption; a moment they will never forget.

Kamala Harris has made history by becoming the first woman to be elected to office in the White House.

In her first speech as vice-president-elect, she touted her running-mate Joe Biden. "You chose hope and unity, decency, science and yes, truth," she said. "You chose Joe Biden as the next president of the United States of America."

Biden concludes his speech on a note of optimism.

"Let us be the nation that we know we can be. A nation united, a nation strengthened, a nation healed," he says.

"The United States of America. Ladies and gentlemen, there's never been anything we've tried and not been able to do."

He ends: "Spread the faith. Love you all, bless America."

With that, celebrants and family join him on the stage, as fireworks are launched, confetti flies and the strains Tom Petty's "I Won't Back Down" can be heard on the telecast.

"Folks America has always been shaped by inflection points, by moments in time we've made hard decisions about who we are and what we want to be," Biden continues.

"Lincoln in 1860 coming to save the union, FDR [Roosevelt] in 1932 promising a beleaguered country a new deal. JFK in 1960 pledging a new frontier and when Barack Obama made history and told us: 'Yes we can'."

"Our nation is shaped by the constant battle between our better angels and our darkest impulses," Biden continues. "Now, a president's say in this battle matters. It's time for our better angels to prevail."

"Tonight, the whole world is watching America and I believe at best, America is a beacon for the globe."

Image source, Reuters

Biden says the first task is to get the coronavirus pandemic under control. "That's the only way we can get back to living," he says.

"On Monday, I will name a group of leading scientists and experts as transition advisers to help take the Biden-Harris Covid plan and convert it into an action blueprint that will start on January 20, 2021," he says. "That plan will be built on bedrock science."

He says he will "spare no effort" to turn the pandemic around.