If you're looking for a refresher or trying to understand it for the first time, we have a guide to the US election that will help.

The US president has a huge influence on people's lives both at home and abroad, so when the next election is held on 3 November, the outcome will matter to everyone.

The US political system is dominated by just two parties, so the president always belongs to one of them.

The Republicans are the conservative political party in the US and their candidate in this year's election is President Donald Trump, who is hoping to secure another four years in power.

The Democrats are the liberal political party in the US and their candidate is Joe Biden, an experienced politician best-known for serving as Barack Obama's vice-president for eight years.

Both men are in their 70s - Mr Trump would be 74 years old at the start of his second term, while at 78, Mr Biden would be the oldest first-term president in history.

The whole election process can be confusing, and the BBC has been helping make sense of it all by answering a range of your questions.

You can read our guide in full here.

Social media isn't an accurate barometer of opinion, but it does give interesting snapshots into how people respond to political moments.

Our misinformation reporter Shayan Sardarizadeh has been looking at the most shared tweets by prominent figures during the debate.

So far, the most popular is a tweet by Joe Biden, demanding that Donald Trump release his tax returns or "shut up about corruption". (Read more on Trump's taxes here.)

The second and third are by right-wing commentators Ben Shapiro and James Woods. Shapiro suggests that Trump scored a victory in an exchange about climate change: "Trump got Biden to admit he wants to end the oil industry. Wild," he said. (See the candidates' climate policies.)

Woods, meanwhile, argued that the debate moderator, Kristen Welker, was biased towards Biden - a popular claim by pro-Trump supporters, but one denied by Welker.

And CNN fact-checker Daniel Dale also raked in a lot of shares in his tweet that accused Trump of "lying" more in this debate than the first.

Read our fact-check of the debate.

Reality Check

President Trump repeated his claim that Joe Biden wants to ban fracking - the controversial process of drilling below ground and using high-pressure water to force out gas.

Mr Biden said: "I have never said I oppose fracking".

However, in March 2020, during a Democratic debate, he said "No more — no new fracking."

He later clarified it: "I said I would not do any new leases on federal lands."

Mr Biden's campaign site says the Democrats would protect "America's natural treasures by... banning new oil and gas permitting on public lands and waters." But they are not opposed to fracking more generally.

• What is fracking and why is it controversial?

Marianna Spring
Specialist disinformation reporter

Somewhat incredibly for a campaign that has been so full of rumours and misinformation, this debate was quite restrained.

Early on, Donald Trump and Joe Biden traded claims about foreign entanglements – accusing each other of getting illicit money from Russia, Ukraine and China.

For several minutes the debaters painted a frankly confusing world map of slush funds and dodgy deals – difficult to understand and in mostly impossible to fact check.

One specific allegation revolves around influence peddling by Mr Biden’s son, Hunter. It emerged from a New York Post story with questionable sourcing that has been somewhat throttled by social media companies.

The president could have gone much darker and brought up more vile rumours swirling online. But he didn’t.

Apart from the chopped word salad that was the foreign influence discussion, other claims were somewhat easier to check.

For instance, a number of popular posts falsely suggest that Mr Trump responded “good” after Joe Mr Biden made a comment about migrant children separated from their parents at the US border.

In the clip, the president actually says “go ahead” to the moderator, hoping to get to the next topic.

Reality Check

In a testy exchange with Trump over law and order, Biden said: “We commuted over 1,000 people's sentences...... the federal prison system was reduced by 38,000 people under our administration.”

Biden is right about the number of commutations during the Obama administration (when he was vice-president) but not about the federal prison population.

About 1,700 inmates had their sentence commuted, external by Obama and a further 212 received a pardon.

But in 2016, the last year Obama and Biden were in office, there were 16,500 fewer inmates in the federal prison system, external compared to 2009.

The prison population fell in the final three years of the Obama administration and has continued to decline under Trump.

Image source, Reuters

If social media is to be believed, there was only one winner of last night's debate - the woman in charge.

Kristen Welker has been lauded online for her performance as moderator, in particular for keeping candidates to time and not allowing them to talk over her.

There have been more than 125,000 tweets about the 44-year-old NBC journalist, who became only the second black woman to moderate a presidential debate alone, 28 years after ABC News journalist Carole Simpson became the first in 1992.

Welker would have still been at school when Simpson moderated that debate between Bill Clinton and George HW Bush.

You can read more about the woman of the moment here - including some unexpected praise from the president, who had criticised Welker heavily before the event.

National polls are a good guide as to how popular a candidate is across the country as a whole, but they're not necessarily a good way to predict the result of the election.

In 2016, for example, Hillary Clinton led in the polls and won nearly three million more votes than Donald Trump, but she still lost - that's because the US uses an electoral college system, so winning the most votes doesn't always win you the election.

With that caveat aside, Joe Biden has been ahead of Donald Trump in most national polls since the start of the year. He has hovered around 50% in recent months and has had a 10-point lead on occasions.

Read more: How are Trump and Biden doing in the polls?

Image source, Reuters

If you're just waking up in Europe or catching up at lunchtime in Asia, welcome to our coverage of last night's presidential debate. Here's what you need to know:

• Firstly and most strikingly - the threat of the mute button (explained here) seemed to have the desired impact. This was a much calmer, less disruptive debate than the event three weeks ago, where Joe Biden snapped "Will you shut up, man!" at Donald Trump, and the president snarked: "There's nothing smart about you, Joe."

• Trump claimed a coronavirus vaccine would be ready "in weeks" and boasted that he was now "immune". When he said people were "learning to live" with the disease, Biden pounced with one of the memorable lines of the night. "He says we're learning to live with it. People are learning to die with it."

• Trump brought up allegations that Biden personally profited from his son Hunter's business dealings in Ukraine and China - which his opponent flatly denied, changing the subject to Trump's taxes and business ties to China. (If you need a refresher - here's what Hunter Biden was doing in Ukraine and China)
• There was no repeat of Trump's controversial moment from the last presidential debate, where he talked himself into trouble over white supremacist groups. Instead, he targeted Biden for sponsoring a 1990s crime bill that led to a sharp rise in the number of black Americans in prisons.
• It's probably fair to say both candidates did what they hoped to going into this debate: Trump was less combative but still hammered his point about Biden's son, while Biden set out his vision for four years in charge
• If you ask the internet who won, the answer is moderator Kristen Welker, the first black woman to moderate a presidential debate alone since 1992. She asked for civility and order, and largely got it. “I’m jealous,” concluded Chris Wallace, the moderator of last month's acrimonious encounter.
• Since both candidates made some misleading claims, we've fact-checked what they said here

Reality Check

Defending his handling of the coronavirus pandemic, President Trump said “2.2 million people, modelled out, were expected to die.”

This is a misleading claim.

The figure is mentioned in a study published by Imperial College London , externalin March in the case of an "unmitigated epidemic".

But the study describes 2.2 million deaths from Covid-19 in the US not as the “expected” number, but instead what would occur “in the (unlikely) absence of any control measures or spontaneous changes in individual behaviour”.

So far, there have been more than 223,000 Covid-19 deaths in the US and the 7-day average of daily deaths is still in excess of 760.

Anthony Zurcher
BBC North America reporter

Image source, Reuters

The mute button, or at least the threat of it, seemed to work. In the second presidential debate. Donald Trump and Joe Biden candidates were more restrained.

The candidates allowed each other to speak. They used respectful tones. Even when they went on the attack, they did so in a calm, deliberate manner.

After a pugnacious first debate, during which Trump's constant interruptions may have cost him support in subsequent opinion polls, the president has very visibly dialed down the volume - and it made him a much more effective debater.

This time, the content of what the candidates are saying might be what the American public remembers from the debate - not the chaotic manner in which it was delivered.

Read Anthony's full analysis - and roundup of key takeaways - here.

Image source, Getty Images

Who voters think came out ahead tonight will likely hinge on their party of choice. But according to three snap polls - from CNN, Data Progress and US Politics - Joe Biden was victorious.

In each, more than 51% of respondents declared Biden the winner, with Trump getting the nod from just more than 40% of those surveyed.

Looking for the bigger picture?

Here's a look at how the candidates are faring in national polls.

No worries if you missed some - or all - of tonight's debate. We've rounded up the best bits for you.

Image source, Reuters

Asked how he thought the debate went, Joe Biden told reporters: "Well, that's for the public to judge. I felt good about it, and I thought the moderator did a great job of making it run smoothly, so it was much - much more rational debate than the first one. Got a chance to speak to the American public more, so thank you all very much."

His team were less circumspect in their post-debate briefing, however, claiming the evening was a "dramatic and resounding victory" for the Democrat.

Their message is that the former vice-president is the only candidate with the temperament to lead - and had one of the lines of the night on the coronavirus: "220,000 Americans dead. Anyone responsible for that many deaths should not be president."

Trump blew his "last shot to present a coherent vision - to earn their vote," they said. He desperately needed a huge win, and didn’t get one. His voice was calmer and he did attack a little less, they say - but he did lie."

"Kristen Welker [the debate moderator] gave Trump every opportunity to talk plans, give his vision, and to make a positive case. We got nothing," the campaign said.

"This is a referendum on Donald trump’s presidency – he has never given a case to be re-elected, because he does not have one."

Reality Check

When discussing health care policy, President Trump said: “I have a plan to help people with pre-existing conditions."

If the president does have a plan, he yet to share details of it.

The Affordable Care Act (ACA), passed under President Obama, made it illegal to deny healthcare coverage to people with pre-existing medical conditions.

The Trump administration has sought to repeal it and now seeks to dismantle the law in the Supreme Court.

The president has said he would replace the act with something better and protect people with pre-existing conditions, but his plan to do this is yet to be published.

In September, President Trump did sign an executive order which said: "access to health insurance despite underlying health conditions should be maintained".

But there is no detail about how this will be done or funded.

Laura Trevelyan
BBC World News America presenter, Nashville, Tennessee

Tonight was a more substantive debate than the chaotic first meeting in Cleveland. Biden said he was committed to a fifteen dollar minimum wage, to providing a path to citizenship for 11 million undocumented immigrants, and to a national mask mandate to curb coronavirus. Trump offered no new policies on covid - but personally attacked Biden’s son Hunter, saying without being specific that the Biden family had corruptly benefited from foreign business dealings.

The Trump campaign seized on Biden’s statement that he would transition away from oil, claiming it would cost millions of jobs. The Biden campaign says there’s nothing new in that statement about moving away from oil.

The president wanted this debate to provide a Ronald Reagan moment - that is, a reset, one that would give him a 10 point bounce in the polls. It’s hard to see what that moment was. With more than 47 million Americans having already voted, and very few undecided voters, will this have changed minds?

Both campaigns came away with sound bites for the morning shows and their respective campaign adverts - it’s all down to turnout in the eleven days between now and 3 November.

Trump campaign spokesman Tim Murtaugh has just held a call with reporters where he called the debate a "win" for his boss, and cast the race as a contest between "the reformer and the swamp".

To remind you, Trump ran on a campaign to "drain the swamp" of Washington DC corruption in 2016, and spoke tonight of "you politicians" in an effort to cast himself as an outsider still.

During the call, Murtaugh said Trump's biggest victory was when Biden "pledged to end the oil industry”.

“You can see, physically, Joe Biden realised he made a grave error.”

In an exchange about North Korea, Joe Biden branded its leader Kim Jong-un a "thug" and accused Donald Trump of legitimising the pariah state.

As Trump hit back, saying it's a positive thing to have good relationships with the leaders of other countries, Biden made a comparison that's raised a few eyebrows.

The reaction is coming in. Let's take a look at the Twittersphere first.

Conservatives were praising President Trump's performance in general. Commentator Ann Coulter said she was "amazed".

But as another conservative, author Rod Dreher pointed out - the debate was unlikely to have changed many minds.

On the other side, Nelba Marquez-Greene, a gun control advocate who lost her daughter in the Sandy Hook school shooting, was more critical of Trump's performance.

And actor Mark Ruffalo, who campaigned with the Democratic ticket this week, declared that "#BidenWon".

Reality Check

Trump has often said that the worst is over with coronavirus pandemic. In tonight’s debate he reasserted this, claiming the US was “rounding the turn, we've rounded the corner”.

But the latest numbers show a rise in cases and hospitalisations in the US, and deaths remain high.

The White House’s top infectious disease expert, Dr Anthony Fauci has called the latest statistics “disturbing”.

Around 60,000 new daily coronavirus cases are being reported across the US, up from around 50,000 a day at the start of October, according to the Covid Tracking Project., external

Hospitalisations have also increased by more than 30% since the start of the month. Confirmed deaths have remained around 800 a day through October - but there is usually a two to three week lag between increases in hospitalisations and Covid deaths.

Laura Trevelyan
BBC World News America presenter, Nashville, Tennessee

Tom Perez chairman of the DNC tells me Donald Trump had nothing to say on coronavirus in the debate, and attacked the business dealings of Joe Biden’s son Hunter because he has no agenda for his second term.

As the Trump campaign attacks Joe Biden for saying during the debate he’ll transition away from oil and that will cost millions of jobs, Tom Perez says there’s nothing new in that statement and it’s part of the president’s deflection from his own record.