Ron Christie is a Republican political strategist, who also worked as a member of former Vice-President Dick Cheney's staff.

He tells BBC News that both campaigns should have set out their visions more clearly and politely.

"In these troubling times, the American people are looking for a bit more civility from their elected or soon to be elected officials."

Both campaigns need to "take a step back, go back home, and reflect," he says.

"They did a disservice to the American people," he said.

"They probably turned off many more voters than they energised tonight."

Image source, Reuters

As we sift through the reaction from that feisty first debate, here's a look at how Democrats and Republicans are feeling about it.

Senate Democratic leader Chuck Schumer focused on the pandemic and climate change in his criticisms of Trump, while Senator Amy Klobuchar (you may recall her presidential run earlier this season) honed in on Trump's failure to condemn white supremacy outright.

Republican Senator Rand Paul, meanwhile, accused Biden and his party of wanting to shut down the US in response to the pandemic. Conservative commentator Candace Owens took a sceptical view of the whole evening.

Reality Check

Trump said an increase in postal ballots is going to cause "fraud like you've never seen”.

As a consequence of the coronavirus pandemic, many US voters are expected to use postal voting for this year’s presidential election.

The president has repeatedly warned that this will lead to widespread cheating. There have been isolated cases of fraud including recent examples in North Carolina and New Jersey.

In September the US Department of Justice released a statement, external about an incident in Pennsylvania in which "nine military ballots were discarded" and that seven of them "were cast for presidential candidate Donald Trump".

But numerous studies have not revealed evidence of major, widespread fraud. The rate of voting fraud overall in the US is between 0.00004% and 0.0009%, according to a 2017 study by the Brennan Center for Justice., external

Read more:

Do postal ballots lead to voting fraud?

Image source, Getty Images

A snap viewer poll by CBS News, BBC News' US partner, named Joe Biden winner of the first, messy 90-minute tussle of a debate between the candidates.

Of those polled, 48% say Biden won, while 41% say the title should go to Trump and 10% saw the night as a tie.

Commentators say that after a nasty night, the real loser was the country - and the poll seems to say the same.

Tonight's debate made 69% of voters feel annoyed, and 19% feel pessimistic. On a more positive note: 31% were entertained and 17% say they were informed.

Democratic political analyst Mary Anne Marsh gives her view of the clash to BBC News, declaring: "There was a debate, and a wrestling match showed up instead!"

Is there even a point in having two more presidential debates if they take this combative, muddled form?

Some have suggested simply muting the candidates' mics if they can't stop talking over each other.

Marsh says that would play into the president's narrative of distrust: "If you cut his mic, he'll say he's being silenced and he's being cheated."

She adds that she will be interested to see how many voters gave up and switched off during the first half hour of the debate.

Alright, as things continue to heat up off-stage as we all process the last 90 minutes, let's take a look back at some of the key moments from tonight.

• In what was certainly one of the most chaotic presidential debates in modern history, we saw clashes not only between the candidates but between the president and the moderator. Chris Wallace had to beg for an end to the cross-talk and scolded the president for ignoring the rules .
• Between Biden and Trump, the biggest battles were over Covid-19, the economy, election integrity and race.
• Biden criticised Trump's pandemic response while Trump touted his economic prowess and promised it would bounce back. Biden called for Trump to release his returns while Trump said Biden was responsible for the tax credits he's used in the past.
• In one notable exchange that's sparked anger on social media, Trump claimed most unrest "we're seeing is from the left-wing, not the right-wing" and didn't outright condemn white supremacy.
• And at the end, when asked by the moderator if they'd both concede and urge calm, Biden said he'd wait until the count was independently verified. The president again cast doubt on mail-in voting and told his supporters to "go into the polls and watch very carefully".

Anthony Zurcher
BBC North America reporter

The closing segment of the debate was on election security and concerns – presented by both the left and the right – that the election will not be free and fair.

When it came to the details of the discussion- if you can call it that - they mostly revolved around Trump sharing a series of anecdotes which show, he claimed, that mail-in voting is fraught with corruption and incompetence.

“This will not end well,” Trump said at one point – a sentiment that many Americans on both sides of the political aisle will agree with, albeit for different reasons.

Biden, for his part, tried to take the high ground. He called for all the ballots to be counted and promised to respect the results of the election once a winner has been decided. It seemed he had a few more points to make in conclusion, but Trump interrupted him again and then Wallace announced the debate was over.

It was a sudden end to a chaotic evening that can hardly be called a debate in any traditional sense of the word. These events rarely swing an election one way or another, and this one was so muddled it seems unlikely few minds were changed.

Republican strategist Bryan Lanza is giving his verdict on the debate to BBC News live from Washington.

"It was a demolition derby," he says.

"It was hard to understand anyone's cohesive argument," he admits, "(but) that's a disadvantage to Joe Biden."

"...I don't think it showed Joe Biden in a presidential light."

Is this really the best way to choose America's next president?

"No, I think these are soundbites," Lanza says.

"It was like a college football game - the left cheers for the left, the right cheers for the right, and you watch the wreckage take place on the field."

Anthony Zurcher
BBC North America reporter

It was predicted that Donald Trump's objective during this debate was to rattle Joe Biden - and within minutes of the start, it became clear he planned to do this by constantly interrupting the former vice-president.

That made for a series of chaotic exchanges, including Trump questioning Biden's intelligence and Biden calling Trump a clown, shushing him and asking, indignantly, "will you shut up, man"?

Moderating this free-for-all may have been the worst job in America tonight.

Coronavirus proved difficult terrain for the president - but he simply suggested Biden would have made things worse.

Did Biden hurt Trump on his 'hidden taxes'? Not necessarily. When he noted that Trump paid less in federal taxes than schoolteachers, that message - which could have been a powerful attack - got buried in 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.

Read Anthony's full take on who won here

Reality Check

A little earlier, Joe Biden claimed that Trump’s former adviser Kellyanne Conway said “riots and chaos and violence help [the president's] cause".

Trump said he didn’t think she had said that. So what did she say?

In August, Conway said on Fox News: “The more chaos and anarchy and vandalism and violence reigns, the better it is for the very clear choice on who’s best on public safety and law and order.”

She was referring to protests across the US over racial injustice that sometimes turned violent.

"It's been an interesting hour and a half," Wallace says with a laugh. Quite what the American people will make of such an argumentative evening is anyone's guess.

Next up: the vice-presidential debate between Kamala Harris and Vice-President Mike Pence on 7 October in Salt Lake City, Utah.

Trump is seen showing a thumbs-up as Melania Trump and Jill Biden approach the podiums. And that concludes our first chaotic night.

As the conversation turned to the electoral process, Wallace pointed out that in eight states, workers are prohibited from beginning to process postal ballots until 3 November, no matter how early they arrive. So there is a good chance that it could take days, if not weeks, for all of the votes to be counted before a winner is declared.

"Will you urge voters to stay calm and not engage in civil unrest?" asked Wallace.

"I'm urging my supporters to go into the polls and watch very carefully," replied Trump. He referenced a case in Philadelphia where Trump supporters say they were prohibited from monitoring early voting. Philadelphia city officials say the Trump campaign has no registered vote-monitors in the city, and that the public are not allowed to walk into polling centres and demand the ability to conduct oversight.

"Count the ballots," Biden said, adding that he would wait to claim victory until a result was independently confirmed.

When the topic turned to race in America, our voter panel watching the debate fell silent and became more attentive. They were curious to hear if Trump would denounce white supremacy or if Biden would say outright he supported the Black Lives Matter movement.

Keirsten, undecided voter: “I don’t think either one answered the question sufficiently for me. Biden was thorough but didn’t say what he was going to do on systemic racism.”

Brian, undecided voter: “I agree with Keirsten that neither candidate answered the question on race directly. I think a politician should be able to say ‘I don’t support hate groups’, but Trump did not say outright that he wouldn't stand by the Proud Boys.”

Josh, Biden voter: “I agree with what Brian said. It got to a point where Trump was talking over Biden so much that Biden got away with not answering the question."

Ariel, Trump voter: “Keirsten is correct, they kind of got off track. I’m disappointed in what’s happening with President Trump. I’ve heard Trump talk time and time again about race. He truly does care about these things - I’ve heard it out of his own mouth."

Meet the voters we’re watching the debate with tonight.

Reality Check

Biden, the Democratic candidate, has said that even before Covid, "manufacturing went into a hole” in response to Trump's claims about his soaring pre-pandemic economy.

In fact, Biden is wrong, according to the figures.

As of August, there were 237,000 fewer manufacturing jobs in the US than when Trump took office in 2017.

But prior to the pandemic, Trump had added almost half a million manufacturing jobs during his first three years in office.

Another heated exchange from earlier in the debate:

With the debate nearing its end, the topic is turned to climate change, a big subject to cover.

Wallace asks why Trump rolled back environmental protections and what his views are on human-caused climate change.

"It's much less expensive," he says of the regulatory changes, adding that his policies have helped businesses.

Trump says that wildfires in the American West could be solved by having "better forest management" - a claim he has made before.

Pressed by the moderator, he concedes that people are having an effect on the climate.

Image source, Reuters

Biden says he does not support the "Green New Deal" - a controversial Democratic plan to tackle climate change that critics say is too radical and expensive.

The former vice-president says he backs "the Biden deal", his own proposal - but that declaration could well upset the left-leaning base of the party.

As Trump made another pitch as the self-declared "law and order candidate", he said that the "Portland Sheriff" supported him - naming the Oregon city that faced 100 days of unrest this summer.

It's a strong endorsement. The problem? It's not true - according to the Multnomah County Sheriff - the county that encompasses Portland.

Sheriff Mike Reese took to Twitter to say he had "never" supported Trump, and had no plans to do so.

Anthony Zurcher
BBC North America reporter

When time came to talk about law and order, both candidates proved vulnerable to sharp questions by moderator Wallace.

When asked about whether, as the self-professed leader of the Democratic Party, he had called on the mayor of Portland or the governor of Oregon to take steps to stop the unrest in that city, Biden demurred, saying he no longer held elected office.

Trump, for his part, was offered the chance to directly renounce right-wing violence from white supremacists and militias. He said he would, but then he didn’t, instead pivoting to attack Antifa and left-wing "mobs".

Wallace was giving both candidates a chance to cut against their own bases, which can at times be a wise political strategy. Instead, they both dodged and dissembled.

Image source, Getty Images

Trump is asked if he is willing to denounce white supremacists and militia members who have further inflamed protesters against racial injustice around the country.

"I would say almost everything we're seeing is from the left-wing, not the right-wing," Trump claims, even as both Biden and Wallace urge him to denounce supremacist groups.

"Proud Boys, stand back and stand by," he says, referring to the "men's rights" group that has clashed with protesters in Portland and other US cities.

He then say the real threat comes from antifa - a loose coalition of left-wing anti-fascist protesters - and warns that they will instigate a coup if Biden wins.

On Twitter, most commenters agree that Trump did not fully denounce white supremacist groups despite saying that he was willing to do so.

More about these groups and what they believe here...

Anthony Zurcher
BBC North America reporter

If there’s a message the Trump campaign wants Americans to take away from this debate – a clip that was tweeted out from the president’s account even as the debate was ongoing – it’s that Joe Biden had almost half a century in public office to solve the problems facing the country, and those problems are still around.

“In 47 months, I’ve done more than you’ve done in 47 years,” Trump told the vice-president.

Biden’s response came later in the debate.

“Under this president, we’ve become weaker, sicker, poorer and more divided,” he said.

After that, Trump interrupted and the debate turned into a scuffling match between moderator Wallace and the president.