Image source, Getty Images

Let's get some numbers now. Joe Biden is projected to win the White House, after securing the 270 electoral college votes required to become president. Currently he has 279 to Trump's 214 with four states left to call.

Biden's also leading in the national popular vote, which has ticked up since Tuesday night as more and more postal votes were counted.

The Democrat now has around four million more votes nationwide than Donald Trump - 74,523,622 votes compared to 70,356,852.

Biden has won the most votes of any candidate on record, partly due to the highest turnout in about a century. Meanwhile Trump won more votes than he did in 2016 - in turn winning the second highest number in history.

Messages for Biden have poured in from across the world but his biggest supporters are closer to home.

Biden's wife Dr Jill Biden and his granddaughter Naomi both tweeted within hours of the announcement, sharing photos of themselves with the future president.

VP-elect Kamala Harris's husband, Doug Emhoff, also shared a photo of the moment they found out the news - while out on a walk in Delaware.

Her sister Maya also tweeted her, congratulating her on her historic win.

Image source, Reuters

As we've mentioned in previous posts, Kamala Harris has made history today in several ways.

She is the first female US vice-president-elect, and is set to be the first black person and the first Asian American to serve in the VP role.

The Center for American Women and Politics (CAWP) said it was an "enormously significant moment in the story of women's participation in American politics and in the history of our country".

CAWP director Debbie Walsh said it was "all the more symbolic" that it happened in the year of the 100th anniversary of the 19th amendment, which guaranteed American women the right to vote.

"Her win puts to rest the question of the electability of women to high office - a question that haunted both the women and people of color who ran for the Democratic nomination this cycle," she said.

"To women and girls of all walks of life, of every political persuasion, Harris's ascension to the vice presidency broadens the horizons of the possible."

Read more about what her experience tell us about US politics.

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.

Teresa Lewis, 60, from Idaho asks: Can the president run again in 2024?

In a word: yes. In the US, presidents are allowed to serve two terms of four years each - and they don't have to be back-to-back.

As Trump now joins nine other US presidents who lost their re-election bids, he is within his rights to run again.

And he wouldn't be the first to do so.

America's 22nd president, Grover Cleveland, was first elected after the Civil War in 1885. He was defeated in his 1888 campaign after winning the popular vote but losing the electoral college.

But he moved back to the White House in 1892, serving out his second term after a four-year gap.

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

Image source, Reuters

We're now waiting to hear from Joe Biden, who will address the nation for the first time as president-elect. He'll be joined by Kamala Harris, the vice-president-elect.

Their spouses, Jill Biden and Doug Emhoff, are also going to join them on stage.

The event in Wilmington, Delaware is expected to start at 20:00 ET (01:00 GMT) - so it's fair to say we've got your Saturday night sorted.

Anthony Zurcher
BBC North America reporter

After nearly 50 years in public office, and a lifetime of presidential ambitions, Joe Biden has captured the White House.

These are the five reasons he finally won the presidency.

1. Covid, Covid, Covid

Perhaps the biggest reason Biden won the presidency was something entirely out of his control.

The pandemic and the subsequent economic decline knocked Trump off his preferred campaign message of growth and prosperity. It also highlighted concerns that many Americans had about his presidency, over its occasional lack of focus, penchant for questioning science, haphazard handling of policies large and small, and prioritisation of the partisan.

2. Low-key campaign

Over the course of his political career, Biden established a well-earned reputation for talking himself into trouble.

In his third try for the Oval Office, Biden still had his share of verbal stumbles, but they were sufficiently infrequent that they never became more than a short-term issue.

3. Anyone but Trump

Biden bet his political fortunes on the contention that Trump was too polarising and too inflammatory, and what the American people wanted was calmer, steadier leadership.

Democrats succeeded in making this election a referendum on Trump, not a binary choice between the two candidates.

Image source, Reuters

4. Stay in the centre

During the campaign to be the Democratic candidate, Biden's competition came from his left.

Despite this pressure from his liberal flank, Biden stuck with a centrist strategy, refusing to back universal government-run healthcare, free college education, or a wealth tax. This allowed him maximise his appeal to moderates and disaffected Republicans during the general election campaign.

5. More money, fewer problems

From April onwards, the Biden campaign transformed itself into a fundraising juggernaut, and - in part because of profligacy on the part of the Trump campaign - ended up in a much stronger financial position than his opponent.

At the beginning of October, the Biden campaign had $144m more cash on hand than the Trump operation, allowing it to bury the Republicans in a torrent of television advertising in almost every key battleground state.

The president has taken to Twitter - again - to weigh in on his opponent's win.

Trump rehashed a couple of inaccurate claims about the election, earning him another Twitter warning on his message.

He claimed "observers were not allowed into the counting rooms", but this is false. Watchers from both parties were allowed inside counting areas.

He added that "bad things happened which our observers were not allowed to see", though some of his lawyers have previously acknowledged they were present for the counting.

There is no evidence of widespread fraud. Election officials across the states have said the process has unfolded smoothly.

The president did note he won the most votes of any sitting president - this is true. He's right behind Biden, who broke the record for most votes in history.

BBC Monitoring
The world through its media

There is a range of views over the result in Latin America, reflecting the polarised attitudes towards the current US president in the region.

Colombian news magazine Semana carried the headline "The end of the nightmare", while in Mexican daily Excelsior, columnist Julio Faesler predicted a new "suaveness of style" under Biden, which will contrast starkly with the "crude" Trump era.

Bolivia's left-wing former President Evo Morales said on Twitter it was a "defeat of racist and fascist policies", as well as the "inhuman attacks on Mother Earth" alluding to the US withdrawal from the Paris climate agreement.

Argentina's Clarin said that Biden "knows the region well and will try to deepen ties and focus on a democratic transition in Venezuela".

Meanwhile, commentators in Brazil and Colombia, whose right-wing presidents had expressed support for Trump, are reflecting on what Biden's win would mean for their country. Leading Brazilian daily O Globo ran the online headline: "Trump's defeat threatens right-wing axis with Brazil and Colombia".

However, elsewhere in Colombia, the first female mayor of the capital Bogota, Claudia López, tweeted a special greeting to Vice President-elect Kamal Harris, saying: "With every woman that wins, we all win. The change is unstoppable".

White House spokeswoman Kayleigh McEnany is criticising Democrats for not asking supporters who have taken to the streets to celebrate Biden's win - despite the pandemic - to social distance.

She tweeted a video from a CNN journalist at the White House, showing protesters dancing to the YMCA, a popular song Trump used to end his large in-person rallies, where many did not wear masks.

Our reporter at the scene, Marianna Brady, says the news fell on a warm sunny day in the nation's capital, which has felt like a ghost town since lockdown measures began in March.

People are popping bottles of champagne, and dancing and cheering. Although nearly everyone is wearing a mask, there is little social distancing happening.

Image source, Reuters

The Ayrshire Daily News, which reports on the region of Scotland where Trump's Turnberry golf resort is located, is taking a rather different view of today's news out of the US.

"South Ayrshire Golf club owner loses 2020 presidential election," reads, external their witty headline.

Meanwhile, the Glasgow-based Daily Record, external reports that gambling bookies heavily suspect that the soon-to-be-former president will come to Scotland to play golf in order to help get over his loss.

Laura Trevelyan
BBC World News America presenter

Young voters in Washington DC say they are overjoyed to see Trump go.

One absentee voter, a university student from Pennsylvania, says she was so excited to vote that she nearly went all the way back to cast her ballot in-person at the state that handed victory to Biden hours ago.

Anthony Zurcher
BBC North America reporter

Joe Biden has declared victory in the 2020 presidential election, but Donald Trump has pledged to continue to contest the results. If his efforts are unsuccessful, however, the pressure on him to publicly concede defeat will mount. Does he have to?

The concession phone call from a losing candidate to the victor is a respected tradition of American politics. It is by no means obligatory, however.

In 2018, for instance, Democratic governor candidate Stacey Abrams claimed voter fraud and intimidation and never conceded to Brian Kemp, her Republican opponent.

That’s never happened in a modern presidential race. But as in Georgia, as long as election results are legally processed and certified, the machinery of government will grind on, regardless of what Trump does.

While Trump doesn’t have to concede, or even put on a good face and attend Biden’s inauguration ceremonies, he does have some legal obligations. He must authorise his administration to make preparations for Biden’s team to take over. That is something, according to Trump officials, the president has already done.

Trump ascended to the presidency as an unconventional candidate unafraid to break with long-established norms. If he so desires, he could exit the office that way, as well.

Image source, Getty Images

Biden's plans for the next four years are going to face some severe roadblocks ahead, as Republicans have claimed key victories in Congress.

It's a situation that many analysts say leaves the most ambitious parts of his agenda dead on arrival.

So how will he save the economy, fix inequality, address climate change and take on China and Big Tech?

Good question.

Read more here:

Five questions for Joe Biden on the economy

Image source, Reuters

We told you earlier what a Biden presidency could mean for relations with China and Russia, now let’s look at North Korea and Israel.

North Korea

North Korea once described Mr Biden as a "rabid dog" - but now Kim Jong-un will be making careful calculations before trying to provoke the new US president, writes Laura Bicker in Seoul.

It's likely Chairman Kim would have preferred another four years of Donald Trump.

The leaders' unprecedented meeting and follow-ups made for incredible photo-ops for the history books but very little of substance was signed. Neither side got what they wanted out of these talks: North Korea has continued to build up its nuclear arsenal and the US has continued to enforce strict sanctions.

In contrast, Joe Biden has demanded North Korea show that it is willing to abandon its nuclear weapons programme before he holds any meetings with Kim Jong-un. Many analysts believe that unless Biden's team initiates talks with Pyongyang very early on, the days of "fire and fury" may return.

Israel

There are expectations of a reset of much of Donald Trump's Middle East policy, writes Tom Bateman in Jerusalem.

President Trump supercharged the two poles of the Middle East. He sought to reward and consolidate America's traditional regional allies, while isolating its adversaries in Tehran.

President-elect Biden will try to rewire US Middle East policy back to the way he left it as Vice-President under Barack Obama: Easing Trump's "maximum pressure" campaign on Iran and aiming to re-join the 2015 nuclear deal abandoned by the White House two years ago.

That prospect horrifies Israel and Gulf countries like Saudi Arabia and the UAE.

The result also dramatically shifts the US approach to the Israeli-Palestinian conflict.

Read more about what this means for these countries and others here.

Senator Chuck Schumer, the top Democrat in the Senate, has just taken a drive through Brooklyn to see some of the cheering Biden supporters in the streets.

Holding up his phone for Biden to hear, revelers cheered and shouted "thank you, Joe!"

Tara McKelvey
BBC News, Washington

Image source, Getty Images

The president has returned to the White House after an afternoon at his golf course.

He ducked into the West Wing, entering the building discreetly through a doorway on the side.

As he headed towards the door, his shoulders were slumped and his head was down.

Then he looked over and saw me and a few other journalists, members of the pool, a group of reporters that travel with the president.

He gave me and the other reporters a thumbs-up sign and went inside.

Still he did not look like himself: the swagger was gone for a moment, and he seemed subdued.

I am outside of the White House now, waiting to see if he will make another appearance - or decide to talk to me and my colleagues here at the White House on this extraordinary day.

Image source, Reuters

During Donald Trump's four years in office, the US’s relationship with the world changed profoundly.

Here, our correspondents explain what a Biden presidency could mean for relations with China and Russia.

China

Joe Biden's victory offers another challenge for the Chinese system, writes John Sudworth in Beijing.

You might think Beijing would be glad to see the back of Donald Trump. As China-basher-in-chief he hit them with a trade war, levied a raft of punitive sanctions and badgered and blamed them for the coronavirus pandemic.

But some analysts have suggested that the Chinese leadership may now be feeling secretly disappointed. Not because they have any lasting fondness for Trump, but because another four years of him in the White House held out the tantalising prospect of a bigger prize. Divisive at home, isolationist abroad - Trump seemed to Beijing the very embodiment of the long-anticipated and hoped for decline in US power.

China might, of course, try to find advantage in Joe Biden's willingness to seek co-operation on big issues like climate change. But he's also promised to work to repair America's alliances, which may prove to be far more effective in constraining China's superpower ambitions than Trump's go-it-alone approach.

Russia

A more predictable administration may be the "silver lining" for Russia of Biden's win, writes Steven Rosenberg in Moscow.

The Kremlin has an acute sense of hearing. So when Joe Biden recently named Russia as "the biggest threat" to America, they heard that loud and clear in Moscow.

The Kremlin also has a long memory. In 2011 Vice-President Biden reportedly said that if he were Putin, he wouldn't run again for president: it would be bad for the country and for himself. President Putin won't have forgotten that.

Moscow fears the Biden presidency will mean more pressure and more sanctions from Washington. With a Democrat in the White House, could it be payback time for Russia's alleged intervention in the 2016 US election?

But for the Kremlin there could be a silver lining. Russian commentators predict a Biden administration will, at least, be more predictable than the Trump team. That might make it easier to reach agreement on pressing issues, like New Start - the crucial US-Russian nuclear arms reduction treaty due to expire next February.

Read more about what this means for the rest of the world here

Image source, Pete Souza

Joe Biden's old boss Barack Obama has released a statement, external saying: "I could not be prouder to congratulate our next President, Joe Biden, and our next First Lady, Jill Biden."

"I also could not be prouder to congratulate Kamala Harris and Doug Emhoff for Kamala's groundbreaking election as our next vice-president."

The 44th US president pointed to the record number of voters backing the Biden-Harris ticket, which he says gave them a "historic and decisive victory".

Obama says that his former vice-president is prepared to handle all of the "extraordinary challenges" that he will inherit in January including "a raging pandemic, an unequal economy and justice system, a democracy at risk and a climate in peril".

He says Biden will work for Americans who did not support him, and calls for those that opposed him to give him a chance.

It will be up to all Americans, Obama says, not just Biden and Harris, "to lower the temperature and find some common ground from which to move forward".

He also spoke today with both Biden and Harris to offer his congratulations directly.

Hillary Clinton, who worked with Joe Biden when she served as Obama's secretary of state, also congratulated the winners, saying it was a "new page for America".

Eimear Flanagan
BBC News NI

Image source, LAURITA BLEWITT

"Joe Biden told me: 'I'll be back as president.' Please God he will."

Irish plumber Joe Blewitt has more reason than most to cheer a Democratic victory in the US election.

For one, it means he can tell people a famous cousin of his will soon be taking up office as the president of the United States.

For another, his town of Ballina, County Mayo, can hope the new US president-elect keeps his promise and makes his way back to the west of Ireland soon.

If Biden does visit Ireland, he may have to do a bit of a tour to see all his relatives - the Blewitt clan are among several Irish families who claim kinship with the next US president.

Biden's great, great, great grandfather - Edward Blewitt - left Ballina for America during the Irish famine.

Joe and his sister Laurita have met Biden several times and have already visited him in the White House in his role as vice-president under Barack Obama.

It might be 170 years since his ancestors left, but the president-elect is fiercely proud of Irish roots.

In 2016, he said: "Being Irish, without fear of contradiction, has shaped my entire life."

Read the full story here

James Landale
Diplomatic correspondent

Image source, Getty Images

Joe Biden is no stranger to Britain. He has known every prime minister since Margaret Thatcher. At least until now.

For Mr Biden has yet to meet Boris Johnson, a man he’s called a “physical and emotional clone” of Donald Trump. And the two men have their differences.

Mr Biden opposes Brexit. He warned publicly last month that a UK-US trade deal was dependent on Brexit not damaging peace in Northern Ireland. Many observers believe this will mean that when President Biden seeks to repair transatlantic relationships, he may focus more of his attention on Paris and Berlin than London.

There is also scepticism that a trade deal with Britain would be seen as priority. That said, there are issues where Mr Biden’s views align with Britain’s: being tough on Russia; reviving the Iran nuclear deal; agreeing new carbon reduction targets at a big United Nations summit in Britain next year.

A Biden presidency would be more multilateral, renewing US support for the Nato military alliance and the World Health Organization. Allies like Britain would still come under pressure to support America’s confrontation with China. But Mr Biden’s priorities would be overwhelmingly domestic: with fewer military commitments overseas and trade deals coming second to fixing the US economy at home.

So a Biden presidency may not mark a return to America’s global interventionism of the past. But its diplomacy would be calmer and more predictable, with perhaps fewer tweets.