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We hope you tune in for the next election debate - the race for the White House could still go either way.

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Image source, Reuters

We're ending our live coverage of the debate and its aftermath soon. Thanks for joining us for what proved to be an explosive encounter between two bitter rivals for the US presidency.

Before we wrap up, here is a summary of some of the key moments before, during and after the debate in Cleveland, Ohio.

• Trump and Biden traded verbal blows in a chaotic and tempestuous presidential debate that numerous US media outlets said had brought shame to America
• The president frequently interrupted, provoking Biden to tell him to "shut up" and call him a "clown" as the two bickered over the pandemic, healthcare and the economy
• The moderator, Fox News anchor Chris Wallace, struggled to defuse the volatile back and forth, drawing criticism from observers
• When Wallace challenged Trump over white supremacist support, the president refused to condemn a far-right group known as the Proud Boys
• Democrats, led by Biden's vice-presidential running mate Kamala Harris, rebuked the president for his failure to denounce the group when prompted
• But Trump's campaign manager said the president had "turned in the greatest debate performance in presidential history", portraying Biden as "weak" and beholden to "anti-police leftists"
• Ahead of the debate, Biden and Harris released their most recent tax records. Both paid more than the $750 (£580) the New York Times said Trump did in the years 2016 and 2017

For more on the first debate, you can read our news story, analysis and trove of explainers - including those on how the US election works and the latest polling data.

Reality Check

After polls close in the US presidential election, it could take days - or even weeks - to find out if Joe Biden or Donald Trump has won.

Millions more Americans are expected to vote by post because of coronavirus, meaning a delay in counting all the votes is highly likely.

Will the winner be announced on 3 November?

It's very possible that it won't. Although the result of a US presidential vote is usually known on the night of the election, this year is very different with so many votes being cast by post.

In 2016, nearly a quarter of votes were cast by post. It's estimated that this time it could be more than double – around 80 million – as states employ measures to limit the spread of coronavirus.

There are also concerns that the US Postal Service, responsible for delivering the postal ballots, will struggle to cope with the demand. It has faced budget cutbacks and critics of Trump have accused him of deliberately blocking additional funding.

Most states only include ballots received by the time polls close on election day. But some, like California, will accept them as long as they are sent by the day of the election, even if they arrive a week later.

Will Trump try to overturn the results and ask for a recount of sorts?

This is unknown. Trump has made clear his mistrust of the postal voting system and says there will be "tremendous" fraud involved. This could be the basis of a challenge to the result if he loses.

When asked if he would commit to a peaceful transfer of power if he loses the election, Trump said: "We'll have to see what happens". He also said the election result could end up in the US Supreme Court as a result of doubts over the integrity of postal voting.

A recount of votes would certainly delay the outcome, but is not unprecedented. In 2000, a dispute in Florida took more than a month to resolve before George W Bush was ultimately declared the winner.

• Read more: When will we get a result and could it be contested?

Image source, Reuters

With round one of debating over, Trump and Biden are approaching the final strait of the race for the White House.

The presidential election is now just 34 days away, giving Trump and Biden little time to dust themselves down for their next head-to-head clash.

Two presidential debates remain on the agenda:

• 15 October in Miami, Florida
• 22 October in Nashville, Tennessee

Vice-President Mike Pence and Biden's running mate, Senator Kamala Harris, will also lock horns in a debate:

• 7 October in Salt Lake City, Utah

Like the first debate in Ohio, they will all take place from 21:00-22:30ET (02:00-03:30BST), with no commercial interruptions.

Expect more sparks to fly.

This year's US presidential election could come down to results in just a few key states. Most states are tipped to vote one way or another - so we have already assigned 188 votes to Trump and 233 to Biden.

Can Biden wrestle enough away to seize the presidency? Or will Trump romp home to a second term? It's all about the race to 270 electoral votes - and this time you decide.

Play our game to predict whether Trump or Biden will win, external the key states at the election.

Image source, Getty Images

As the presidential election draws closer, you may be asking yourself: how does it all work?

Well, we've put together a really simple guide to the election, which could shape the US and the world for years to come.

By now, you probably know the candidates are incumbent Republican President Donald Trump and Democratic challenger Joe Biden.

When Americans go to the polls on 3 November, they will cast ballots for a group of officials who represent Trump and Biden in the electoral college.

Each state gets a certain number of electoral-college votes partly based on its population. There are a total of 538 votes up for grabs, so the victor is the candidate that wins 270 or more.

This means voters decide state-level contests rather than the national one, which is why it's possible for a candidate to win the most votes nationally - in what is called the popular vote - but still be defeated by the electoral college.

Got it? If not, you can read more about how the electoral college works here.

Voters around the US tuned in to see President Donald Trump and former Vice-President Joe Biden spar in the first presidential debate.

As the exchange came to a close, we asked members of the BBC voter panel how the candidates performed - and if their answers had swayed their vote.

Keirsten, undecided voter: "I definitely think Biden won the debate, but I don't think that was hard to do because there wasn’t a lot that I was expecting from Donald Trump. At the end of the 'day the loser was really us, the American people. A lot of people were expecting this to go the way that it did."

Brian, undecided voter: "I wouldn't call anyone a winner. It was expected to be chaotic, [and] it was chaotic. Trump controlled the message with more interrupting, talking and controlling. Biden withstood it better than I thought he would. He got a little hot in the collar a few times but I didn’t see any big eye-catching gaffes. I thought Biden had a good few moments where he looked directly at the camera and aimed his message at the public. I think both sides will say they win, but it’s like comparing apples to oranges."

Ariel, Trump voter: "I thought nobody won the debate. I really understand that Trump is not a very seasoned politician. When he did his best was when he was talking about his policies, what he’s done and what he’s going to do. But there were other times Biden would say something and he’d try to debunk it."

Josh, Biden voter: "Biden came out on top. He came out with a strong message and I can't tell you enough how much it mattered that he looked into the camera. Trump was disrespecting Chris Wallace. We already knew he's disrespectful but now America all watched him disrespect Chris Wallace at the same time."

Meet the voters we watched the debate with.

Image source, EPA

The Russian government is watching the presidential campaign in the US closely, President Vladimir Putin's spokesman has said in the wake of the first debate.

"But we do not want to make any statements as this could be viewed as an attempt to intervene [into the election process]," Dmitry Peskov told reporters on Wednesday, according to Reuters news agency, external.

"Russia has never, is not and is not going to intervene in US domestic affairs," he added.

That statement contradicts US intelligence agencies, which accused Russia's government of interfering in the 2016 presidential election.

Intelligence chiefs said Russia wanted to help boost Trump's campaign, including by spreading disinformation online, but the Kremlin has denied the allegations.

In August, the head of the National Counterintelligence and Security Center (NCSC) said Russia was among several countries seeking to influence the presidential election this year.

Image source, Reuters

We can bring you some more reaction from Robin Wright, a foreign affairs analyst who has written extensively about the upcoming election.

She has seen many debates in her time, yet none were more dispiriting than this one. It was, she said, "one of the lowest points in presidential debate history".

She said the chaotic bust-up not only raised questions about the future of presidential debates, but the future of America's political system.

"It's hard to absorb what has just happened and I suspect that is even more true of people watching around the world who once thought that America had the kind of democracy, even if flawed, that they aspired to," Wright told the BBC.

"This was not just 90 minutes of chaos," she added. "It was America, the history of America in 2020."

Both Democrat and Republican supporters have been having their say on the presidential debate. Naturally, the reaction has been partisan on both sides.

Here's what some observers told the BBC and other news agencies.

Republicans

Randi Reed is a Republican and a Trump supporter from Nevada. She described the debate as a "kindergarten cat fight".

She said the president's "gunning for the jugular" was "exactly what we expected from Trump - the rude, crude interrupting". "We went in knowing who we were supporting," she said.

Doug Miller has served as a delegate to the Republican National Convention, he told AFP news agency he "thought the president performed very well".

"But I feel for most of the evening, he was not only debating 'Sleepy Joe Biden', he was having to debate [moderator] Chris Wallace, who I think is a total fool," he said.

Image source, Reuters

Democrats

Bilal Aksoy is a student and a registered Democrat voter in Pennsylvania. He said the debate only served to reinforce the views he held about both candidates.

"I knew that Trump didn't believe in science. He refuses to acknowledge climate change and he refuses to act on the global pandemic that we're living through," he said.

Jamal Simmons is a Democratic Party strategist who has worked as an adviser to former President Barack Obama's campaign.

He said Trump missed opportunities to reach out to undecided voters. "I think Donald Trump went out for a boxing match, went out to just clinch it up for as many rounds as he could," he said.

Image source, Getty Images

Reality Check

During an exchange about Biden's eldest son Beau, who served in the US military and died of cancer in 2015, Trump brought up Biden's other son, Hunter.

Trump: "I don't know Beau. I know Hunter. Hunter got thrown out of the military… dishonourably discharged… for cocaine use."

Biden replied that it was not true that his son had been dishonourably discharged.

Hunter Biden was discharged from the US Navy in 2014, and media reports at the time said that a navy drug test had detected the presence of cocaine., external

However, he was not dishonourably discharged, which is the highest level of punishment the military can hand out.

Read more about the claims made throughout the debate here.

"Proud Boys, stand back and stand by," Trump said in response to a question asking him to condemn white supremacist and militia groups.

The Proud Boys is a far-right, anti-immigrant group with a history of street violence against its left-wing opponents.

Trump’s apparent refusal to denounce the group proved to be one of the most controversial and hotly debated moments of the first debate.

In case you missed it, here's a video of the exchange with debate moderator Chris Wallace.

Barbara Plett Usher
BBC News, Washington

Image source, Getty Images

Like Donald Trump, Joe Biden wants to end the forever wars in Afghanistan and Iraq, but he would keep a small troop presence in both to help battle terrorism.

On Russia, the relationship at the top would certainly look different, likely little else. President Trump often seemed ready to personally forgive Vladimir Putin for violating international norms. But his administration punished Russia with sanctions, and that would probably continue under a Biden presidency.

On China there is rare bipartisan agreement to get tough with Beijing over trade and other issues, the question is about tactics. Biden would continue President Trump's policy of countering China's "abusive economic practices", but jointly with allies, as opposed to Trump's preference for unilateral trade deals.

The sharp elbows of the Trump administration have been successful in winning global support for a boycott of Chinese communications technology. That's part of a serious escalation in US efforts to push back against Beijing on many fronts, anchored in accusations that it mishandled the Coronavirus. This campaign is led by Mr Trump's China hawks: strategic competition they call it; strategic confrontation, is how some analysts describe it. Mr Biden would more actively seek areas of cooperation with a rising China.

Vitaliy Shevchenko
BBC Monitoring

Image source, Channel One

The Trump-Biden debate is a lead story on Russian TV this morning, with news bulletins focusing on the chaotic nature of the event.

State TV's Channel One: "A political theatre of the absurd. A verbal duel which has been dubbed the most scandalous in the history of election campaigning in the US… The most important political show in the presidential race has probably never been so chaotic before."

Pro-Kremlin NTV television: "There was no constructive dialogue. The rivals kept interrupting each other and instead of a balanced discussion they chose the path of mutual insults."

Channel 5, St Petersburg: "The rivals have crossed all boundaries."

Pro-Kremlin Ren TV: "The election debate between Biden and Trump has been called America's greatest disgrace."

Presidential debates have captivated Americans for decades. They can be bruising, gruelling and sometimes explosive affairs - as last night's debate between Biden and Trump proved.

Over the years, some debates have stood out more than others.

The first ever televised debate in 1960 pitted young Democratic Senator John F Kennedy against the sitting vice-president, Republican Richard Nixon.

Kennedy's team made sure he looked fresh for the close-ups, while Nixon, who was recovering from an illness, donned an ill-fitting suit and was seen wiping sweat from his brow. Kennedy did see a jump in the polls after the debates, even though we can't say for certain it was due to his prowess.

Image source, Getty Images

In 2000, Democratic candidate Al Gore's debate performance against George W Bush may have cost him the presidency.

His sighing and eye-rolling during his Republican counterpart's responses came across as condescending to many voters (and made it into a Saturday Night Live comedy sketch).

The significance of the first Trump-Biden debate will become clearer when the dust settles.

Now we turn to BBC Reality Check's examination of some of the claims made by Biden during the first debate.

Biden: "We have 4% of the world's population, [but] 20% of the [Covid-19] deaths."

Verdict: This is roughly correct. But looking at coronavirus deaths per capita, there are a number of countries which are worse than the US.

Biden: "Manufacturing went into a hole" before coronavirus.

Verdict: That's not right, according to the figures. Prior to the outbreak, President Trump had added almost half a million manufacturing jobs during his first three years in office.

Biden: "Trump hasn't lowered drug prices for anyone."

Verdict: The average monthly cost of prescription drugs fell slightly in the year to August 2019, although it then rose again.

For a more detailed take on Biden’s claims, see here.

BBC Reality Check has been verifying some of the claims made by both Trump and Biden during the first debate. Firstly, let's look at some of the claims Trump made.

Trump: "We built the greatest economy in history."

Verdict: That's not right - there have been times in US history when the economy was stronger, as the chart below shows.

Trump: Postal ballots increase will cause "a fraud like you've never seen".

Verdict: Studies have not found evidence of widespread fraud, although there have been isolated cases.

Trump: "We're weeks away from a vaccine."

Verdict: There is a "very, very low chance" of an approved vaccine being ready by the end of October, the chief scientific adviser to the US vaccine programme has said.

For more clarity on claims made in the debate, read BBC Reality Check's fuller analysis.

Image source, Reuters

Senator Kamala Harris, Joe Biden's vice-presidential running mate, has rebuked President Trump for failing to condemn white supremacists during the first debate.

In one of the most talked about exchanges of the night, the president was asked by the moderator, Fox News anchor Chris Wallace, if he was prepared to condemn white supremacists.

He initially said he would, but when asked to denounce the far-right Proud Boys group by name, he told those affiliated with it to "stand back and stand by".

Those who support the group later expressed their allegiance to Trump on social media.

In an interview with CNN, external, Harris said Trump's comments illustrated the contrast between him and Biden, who was "not afraid to speak the phrase Black Lives Matter".

"I heard what we all heard, the president of the United States, in the year of our Lord 2020, refuses to condemn white supremacists," Harris said.

"People talk about, 'is he dog whistling?'," she added. "Dog whistling through a bullhorn is what he's doing."

James Robbins
Diplomatic Correspondent

If Donald Trump wins a second term, the only safe prediction is that relations with Britain will remain utterly unpredictable.

Normally, Downing Street and the Foreign Office would have a fair idea what to expect from a re-elected American president and commander-in-chief. With Trump, however, all bets are off.

The certainties are that Joe Biden's promise to take the US back into the Paris Climate Change accord will most definitely not be the path Trump follows. So, British hopes for a far more ambitious and more broadly based outcome from next year's United Nations Climate Change Conference (COP26) in Glasgow - with the US on board again - will be dashed if it's still President Trump in the White House.

More than that, a naturally divisive Trump in his second term will surely not retreat from his open scorn for the global institutions. The longer that remains the case, the more other democracies, including Britain, think they have to lose in competition with the rising power of autocrats and protectionists of varying degree spread around the world.

Publicly, of course, any British prime minister will commit to working very closely with the leader of the United States.

But a second-term President Trump, emboldened by a new mandate and also freed from any constraint imposed by worry over a further electoral test, is hardly likely to be any easier an adversary in the continuing tough negotiations over a new UK/US trade agreement. Chlorinated chicken will remain firmly on the menu America would like to serve up to the UK consumer.

Anthony Zurcher
BBC North America reporter

When the New York Times story, external about Donald Trump's taxes broke on Sunday night, it was viewed as a bombshell - the public was finally getting a look at information the president - in a break with tradition - had withheld for years.

The Times said Trump paid no income taxes at all in 10 of the previous 15 years. The records reveal "chronic losses and years of tax avoidance", the paper said.

When the topic came up in the debate, Trump offered a similar defence to the one he provided in 2016 - that he had paid plenty of taxes and his ability to avoid a larger tax bill was simply his taking advantage of the law.

Biden, for his part, tried to turn the topic into a condemnation of Republican-passed tax reform. While he noted that Trump paid less in federal taxes than schoolteachers, that message - which could have been a powerful attack - got buried in an ensuing scuffle with the president.

If Trump's tax returns have any legs as an issue in this campaign, it won't be because of this debate.