Ahead of the first debate, Biden had been leading in the polls, on a national level and in crucial battleground states.

Biden has hovered around 50% in recent months and has had a 10-point lead on occasions. The latest average of election polls gave Biden a 6.1 lead over Trump, according to data collated by RealClearPolitics, external.

Analysts said Trump needed a strong showing in the first debate to move the needle of public opinion and catch up with Biden. It remains to be seen if Trump did enough in the debate to improve his standing in the polls.

Check out our poll tracker here.

Image source, Reuters

Presidential debates are seen as box-office moments in the American political calendar.

But while debates are likely to change some minds, there is little conclusive evidence that they cause big swings in public opinion.

At this point in the US election cycle, a large number of Americans have probably already decided who they will vote for. A 2019 research paper from Harvard Business School, external bears this out.

The paper looked at the effects of TV debates on 61 elections in nine countries, including the US. It found that 72% of voters made up their minds more than two months before the election, long before candidates squared off.

"There's this perception that debates are this great democratic tool, where voters can find out what candidates stand for and how good they really are," said Vincent Pons, a business professor who co-authored the paper. "But we find that debates don't have any effect on any group of voters."

However, it's worth noting that US presidential elections are often decided by fine margins in battleground states. It's certainly possible that debates could sway a small but significant cohort of undecided voters in the weeks before election day.

Anthony Zurcher
BBC North America reporter

Image source, Reuters

In a debate that was the political equivalent of a food fight, the winner is the man who emerged least covered in slop.

On Tuesday night, that man was Joe Biden - if only because his main goal was to prove to Americans that he could hold up under pressure, that he had not lost a step due to his advancing age. He had to show he could take a pie to the face, metaphorically speaking, and keep his cool.

He mostly met that standard, although it was at least in part because Donald Trump, by his constant hectoring and interruptions, seldom gave the former vice-president a chance to say something truly damaging to his own cause.

Trump needed this debate to shake up a race that is tilting against him.

Nothing about this free-for-all seems likely to alter the dynamics of this contest or change the minds of the one in 10 American voters who say they are still undecided (although perhaps they'll resolve never to watch another one of these).

Read Anthony's full analysis of the debate here.

Trump and Biden didn't hold back in an angry US presidential debate that quickly got personal and ugly.

Amid angry shouting and name calling, the two fought over the pandemic, white supremacy and the economy during the 90-minute forum in Cleveland, Ohio.

As you might expect, Donald Trump's campaign team has claimed victory in the first presidential debate.

"President Trump just turned in the greatest debate performance in presidential history, displaying a command of the facts and control of the conversation," his campaign manager, Bill Stepien, said in a statement, external.

However, while Chris Christie - who was on Trump's "debate prep team" - said Biden did not turn in a "reassuring performance", he also failed to offer a flattering assessment of the president.

"I think on the Trump side, it was too hot," Christie, the former New Jersey governor, told ABC, referring to the president's confrontational approach to the debate.

"With all that heat, you lose the light," he said. "That potentially can be fixed. Maybe, maybe not."

US newspapers and media outlets have given their verdict on the first debate. It is, for the most part, pretty damning. Their headlines reflect the tempestuous nature of the chaotic back and forth between Trump and Biden.

Here is how some reported the debate:

• On the front page of its late edition, the New York Times says "Trump’s heckles" sent the debate "into utter chaos". As a result, any talk of policies and ideas was "downed out", the paper says
• In a similar vein, the Washington Post ran the headline: "Debate plunges into fiery squabbling". One of the paper's reporters, Dan Balz, called the debate a "disputing first face-off and an insult to America"
• CNN gave a similarly withering assessment, summarising the event as an "absolutely awful debate". "It was, in a word, horrendous," CNN’s editor-at-large Chris Cillizza wrote, external
• The Wall Street Journal, external described the debate as a "contentious" and "depressing spectacle" that was "marked by interruptions and insults". "No one expected a Lincoln-Douglas debate, but did it have to be a World Wrestling Entertainment bout?" the paper asked in an opinion piece, external.

Image source, Reuters

Supporters of a fringe, heavily-armed group celebrated online when President Trump mentioned them by name during the debate.

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

The Proud Boys were founded in 2016 by Gavin McInnes, who co-created Vice magazine. An all-male group, they number a few thousand at most. They're big fans of the president.

Their platform, such as it is, includes Trumpian ideas ("glorify the entrepreneur", "close the border") libertarianism ("give everyone a gun", "end welfare") and traditional gender roles ("venerate the housewife").

They're not exclusively a white organisation and like to project a folksy, normal American image, particularly when chatting to reporters.

But they're most well-known for violent street confrontations with their opponents in the anti-fascist movement.

• Read more: When a right-wing activist met a left-wing anti-fascist

We're getting some highly critical reaction from China to the first debate.

Hu Xijin, the editor-in-chief of China's Global Times newspaper, has commented on the quality of the debate, saying the two leaders "obviously did not show an exemplary role to American people on how to engage in debates".

Hu made the comment on Twitter, which is banned in mainland China, but he's active on the platform.

"Such chaos at the top of US politics reflects division, anxiety of US society and the accelerating loss of advantages of the US political system," the tweet reads, external.

In August, he had commented on the age of the two US presidential candidates - Biden is 77 and Mr Trump is 74.

Hu said the "US democracy is going awry, letting two old men compete for the most important position in the US".

Image source, Reuters

If just you’re joining us from the UK or Europe, good morning and welcome to our coverage of the first presidential debate.

The 90-minute debate in Cleveland, Ohio, was a lively affair, characterised by incessant interruptions, insults and sparring over issues ranging from the coronavirus pandemic to violence at protests.

For those catching up, here are some of the key takeaways:

• The debate descended into a shouting match early on, leaving moderator Chris Wallace imploring both candidates, but particularly Trump, to desist talking over each other
• A key moment came an hour in, when Trump refused to denounce white supremacists. He instructed members of the Proud Boys, a far-right group, to, as he put it, “stand back and stand by”
• At one point, the insults became personal when Trump brought up the issue of Biden’s son, Hunter. When Trump suggested Hunter had been thrown out of the military for cocaine use, Biden said his son “had a drug problem” but had “fixed it”
• Biden rubbished Trump's leadership on the coronavirus pandemic, which has killed more than 200,000 Americans. Defending his record, Trump sought to claim a hypothetical President Biden would have done worse
• On the question of disputing November's election, Trump was asked if he would encourage his supporters to be peaceful if results are unclear. "I'm encouraging my supporters to go into the polls and watch very carefully," Trump said

Read our main story, analysis and stay tuned for more reaction.

Trump likes to call him Sleepy Joe, but someone on Biden's marketing team is no slouch.

After the Democrat snapped "Will you shut up, man" at Trump mid-debate, his campaign started selling T-shirts bearing the phrase and an image of the president looking grumpy.

According to The Hill, they moved so fast that the shirts went on sale while the 90-minute debate was still ongoing.

At some points, the presidential debate sounded suspiciously like three men shouting at each other. (At other points they reduced it to two...)

When Joe Biden snapped at Trump - "Will you shut up, man" - some recalled the 2016 presidential debates, when Hillary Clinton was negotiating both Trump and the challenges of being the first female nominee of a major US party.

Lawyer and writer Jill Filipovic took a moment to point out how sexism had dictated what Hillary could and couldn't say - only for the woman herself to weigh in...

Marianna Spring
Disinformation and social media reporter

The Proud Boys, a far-right, anti-immigrant, all-male group, took to social media to celebrate after President Trump told them to “stand back and stand by” during the debate.

Those who support the group expressed their allegiance to Trump on their Telegram channel, sharing videos of Trump's mention, including one with the caption "God. Family. Brotherhood".

The Proud Boys have previously expressed their desire to fight far-left activists Antifa, who Trump has recently accused of being behind violence on the streets, often without evidence.

And Antifa has also been trending on Twitter as many Republican supporters pushed back at Joe Biden’s comments that “Antifa is an idea, not an organisation”. That alludes to unfounded conspiracy theories about Antifa’s role in recent fires and protests.

But the biggest bit of disinformation to circulate online came prior to the debate.

It was an unfounded conspiracy theory that Joe Biden would try to wear a listening devices during the debate and was refusing to let the Trump campaign inspect his ears. Biden’s campaign shot this allegation down.

But they were still pushed in a text message sent by the Trump campaign, after going viral on Facebook and Twitter promoted by notorious conspiracy theory groups.

And the most popular tweets and Facebook posts centre around President Trump saying he secured the endorsement of the “Portland sheriff” - which was then quickly batted down on Twitter by Multnomah County Sheriff Mike Reese.

If you're just waking up in Europe and wondering how the presidential debate went down, fear not: we have clips to catch you up.

Firstly, here's the moment the candidates clashed over the coronavirus pandemic, with Joe Biden accusing Donald Trump of lying about the issues around Covid-19.

"A lot of people died - and a lot more (are) going to die unless he gets a lot smarter a lot quicker,” Biden warned.

Then there's President Trump's attack on the debate moderator Chris Wallace - who tried but frequently failed to control the two speakers - where he declared: "Well, first I guess I'm debating you, not him, but that's ok - I'm not surprised."

Zhaoyin Feng
BBC Chinese, Washington DC

In China, many social media users woke up to the news about the first US presidential debate and saw it as an amusing event. “What a row... It kept me entertained,” one post on the social media site Weibo reads.

Many pointed out that the debate was like a chaotic quarrel. “There’s a difference between debating and fighting, but Trump has turned the debate into a fight.”

People also questioned why the US had ended up with two presidential candidates in their 70s. “As it’s free election, why don’t they elect two younger, more energetic candidates? Can they (Biden and Trump) do this demanding job?”

One Weibo user joked about finding motivation in Biden and Trump’s fiery exchanges. "Two old men in their 70s fired up fighting for a job. Do you have any reasons not to work hard?"

Already among the most talked-about moments of the debate was Donald Trump's apparent refusal to condemn white supremacy when prompted by moderator Chris Wallace.

Instead, Trump called out one group - the Proud Boys - by name, telling the far-right group to "stand back and stand by".

"But I'll tell you what, somebody's got to do something about antifa and the left," he said.

The Trump campaign has said the remarks were a denunciation of the group, but some interpreted the president's comments as a call to arms and, already, the Proud Boys - classified as a hate group by the Southern Poverty Law Center - has responded by embracing the president's remark.

"Standing down and standing by sir," the Proud Boys account posted on Telegram, the social media app. The group also posted videos of Trump's mention, including one with the caption "God. Family. Brotherhood".

"To say the Proud Boys are energised by this is an understatement," Megan Squire, a computer science professor at Elon University who tracks online extremism, told NBC News. "Their fantasy is to fight antifa in his [Trump's] defence, and he apparently just asked them to do just that."

Image source, Reuters

Image source, EPA

Moderating the presidential debates is one of the toughest jobs in journalism, and Chris Wallace was clear beforehand how he wanted it to go:

"I’m trying to get them to engage, to focus on the key issues," he said. "But if I’ve done my job right, at the end of the night people will say, ‘That was a great debate. Who was the moderator?'”

Sadly for him, it proved almost impossible to keep the two rambunctious candidates on topic and out of each other's allotted time.

Hardly 10 minutes in, the Fox News anchor told Trump: “Mr President, I am the moderator of this debate, and I would like you to let me ask my question and then you can answer it,” - a request the president failed to heed.

At one point Wallace appealed to Trump's sense of decency, halting the debate near the midway point and pleading: "The country would be better served if we allowed both people to speak with fewer interruptions. I’m appealing to you, sir, to do it."

Conservative commentators accused the stricken referee of pro-Biden bias and failing to keep control.

Some of his Fox News colleagues were equally unimpressed.

Left-leaning analysts weren't happy either, with former Democratic Senator Claire McCaskill branding the moderator "embarrassing".

Despite agreement on both sides that he lost control, some felt Wallace had been handed an impossible task.

One thing's for sure: when the presidential nominees return for their second debate on 16 October, the next moderator, Steve Scully, is going to have his work cut out. Maybe it's just as well the C-Span correspondent was recently described as "the most patient man on television".

Laura Trevelyan
BBC World News America presenter, Cleveland, Ohio

It was a chaotic, confusing and combative night. For undecided voters seeking clarity, there was little to be had here in Cleveland. Bluster and crosstalk were the hallmarks of this debate, with President Trump ignoring the rules, and attacking his challenger, while Joe Biden insulted his opponent right back.

The president needed to change the dynamic of this race - and while his loyal base of supporters will love his no holds barred approach, it remains to be seen if the older voters and college-educated women who have been slipping away from Trump will return after tonight.

Nervous Democrats who feared their man might stumble and seem out of touch will be somewhat reassured. Policy discussions almost always devolved into cat fights - the loser was the voter seeking an elevated level of discourse.

Image source, Reuters

Here's a look at how long the candidates spent on each topic - and how long each spoke overall - as compiled by our US partner, CBS News.

Coronavirus was the longest segment tonight, with around 20 minutes spent on the pandemic's economic impact, vaccines, masks and Trump's general handling of the crisis.

Next up was race and violence at 17 minutes, followed by election integrity at 11 minutes and climate change with 10 minutes.

Trump spoke - surprisingly perhaps - less than Biden, with around 38 minutes, compared to 43 minutes taken up by the former vice-president.

When it comes to interruptions, however, the president cut in some 73 times. (In 2016, the fact that Trump interrupted then-rival Hillary Clinton 37 times at one debate raised eyebrows - but that was then, this is now.)

Trump also got the lion's share of follow-ups from Wallace, with 15 compared to Biden's four, and had 14 rebuttals to Biden's nine.

Image source, Getty Images

We're still taking stock of the first presidential debate. But here's a bit of detail on how the event wrapped up in Cleveland:

Reporters from inside the debate venue say Joe Biden gave a shrug to his wife, Dr Jill Biden, when they reconvened after the event, with a look that said what a lot of us felt: "That was a lot".

Before leaving - heading back to a suburban home outside of Cleveland where he will spend the night - the former vice-president said something to moderator Chris Wallace. Trump did not.

And once the lights were on, the mostly quiet audience piped up - one yelling "I love Trump".

For the duration of the night, almost all guests wore masks. The exceptions? Members of Trump's family, including the president's son Donald Trump Jr.

We wrapped up the night by asking our voter panel who they thought won the debate - Trump or Biden. Here's what they said.

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 tonight.