Anthony Zurcher
BBC North America reporter

Trump telegraphed early and often that he would make Biden’s son Hunter a topic of the debate, and it wasn’t long before the president brought the former vice-president’s family up. He alleged that Biden personally profited from his son’s business dealings in Ukraine and China, citing recent news stories based on information allegedly gleaned from Hunter Biden’s laptop computer.

Biden’s defence was to change the subject to Trump’s taxes and the president’s own ties to China. It ended up being a "he said, he said" exchange that probably left the casual American viewer confused – culminating in what was clearly an exchange of scripted lines.

“This is not about his family or my family, it’s about your family,” Biden said.

“That’s a typical politician line,” Trump countered, adding that he – by contrast - was not a politician. “Come on, Joe. You can do better than that.”

The topic has now turned to American families, focusing on American families' access to health care. The subject is key for many important constituencies.

Trump, who is aggressively courting suburban women, argues that his “law and order” message has saved cities from urban poverty and criminal migrants.

He’s also likely to tout his tax cuts and his successful efforts to appoint conservative judges - who is mentioned in the question, as his latest nominee, Amy Coney Barrett, is up for confirmation for the Supreme Court.

Reality Check

There was disagreement between the two candidates about whether Biden called the president’s decision to restrict travel from China in January “xenophobic”.

When restrictions on people entering the US from China were announced at the end of January, Biden said it wasn't the time for "Donald Trump's record of hysterical xenophobia", and the next day tweeted a similar message.

The Biden campaign says this wasn't a reference to the measures, but to the president's overall record in office.

Biden has never specifically said he opposed travel restrictions, but he did say in March that "travel restrictions based on favouritism and politics, rather than risk, will be counter-productive".

Eventually in early April, Biden said publicly that he supported them, with his campaign adding: "Science supported this ban, therefore he did too."

Tara McKelvey
BBC News, Washington

Biden calls the leaders of North Korea, China and Russia "thugs" and says that Trump "embraces" them.

Before he took office, Biden and others in Washington were deeply concerned about Trump as commander-in-chief: they thought he would cosy up to the Russian leader, just as Biden says he has done, and they worried about the fact that Trump would have access to the nuclear button.

His relationship with President Vladimir Putin has been unusually close – and for many it is deeply disturbing.

Yet Trump has not caused a nuclear war or any other kind. As president, he has been relatively restrained in foreign policy and reflects the views of most people here: by and large, they do not want the US involved in foreign conflicts.

In contrast Biden believes US troops should play a role in Afghanistan, and as president he would be likely to leave troops there longer than Trump would.

• Senate committee questions Trump nuclear authority

Biden is asked what specifically he would do to punish China for being the country to see the first cases of the coronavirus.

"I'd make China play by the international rules," Biden says, talking about trade and finance instead of the coronavirus.

Trump, asked the same question, says: "First of all, China is paying. They're paying billions of billions of dollars to our farmers."

"Taxpayer money," Biden interjects, saying that the funds came from Americans not the Chinese.

Trump says his actions to slap tariffs on Chinese steel saved the US steel industry.

Biden, using one of his dismissive catchphrases, describes Trump's comments as "malarkey".

We have more here on who China actually wants to win this election.

Image source, Reuters

Biden returns to one of Trump's Achilles' heels - the president's taxes.

Reporting from the New York Times found that Trump paid nearly no US taxes at all for two years, due to enormous losses in the preceding years, and the president has been repeatedly criticised for lack of transparency on his finances.

"I have pre-paid by taxes, tens of millions of dollars," Trump insists, despite refusing for years to release his tax returns.

"The IRS treats me horribly. I get treated very badly by the IRS very unfairly," Trump says, referring to the agency that collects taxes.

Democrats charge that Trump's finances would prove that he owes millions to foreign interests.

You can read more about the story here -or about what the situation says about the tax paid by the wealthy.

Tara McKelvey
BBC News, Washington

A lingering question for this presidential debate is: who has to cut the audio feed for the candidates?

The individual who would make the decision to silence the president or former vice-president – if either interrupts his rival during his two minutes of allotted speaking time - works for the production crew that operates behind the scenes. If their identity is released, they could become the hero or villain, depending upon how you see the new debate rule and the option of using a mute button. Stay tuned.

The national security discussion has turned into a discussion about foreign political influence, with both men flinging accusations at each other.

"I never got any money from Russia. I don't get any money from Russia." Trump says, claiming that Biden's family has been enriched by Russian oligarchs.

"There nobody tougher than me on Russia," Trump says, adding that he's convinced Nato countries to put up more money during his presidency "to guard against Russia".

"They were paying you a lot of money and they probably still are," Trump says to Biden.

He goes on to tout the "horrible emails" found on a laptop allegedly belonging to Biden's son Hunter, who worked for a Ukrainian gas firm while his father was vice-president.

• Hunter Biden: What was he doing in Ukraine and China?

Biden responds: "I have never taken a single penny from any country whatsoever." He says. Trump has been enriched by foreigners, including the Chinese, he says.

Aleem Maqbool
BBC North America correspondent

Image source, Getty Images

To some extent wearing or not wearing a mask now politically identifies a lot of Americans, that has certainly been my experience in meeting conservatives and liberals around the country in recent months. Little in today’s so far civilised discussion on the virus would have changed many minds on the way the president has handled things.

Supporters of the president have told me they don’t blame him for the extent to which the pandemic has touched American lives (even those who have lost relatives to the virus) and Trump tonight said he took responsibility for the response but that coronavirus was not his fault.

Biden waved his mask at a couple of junctures and echoed what many Democrats say; that there were clear mistakes made by the president including hiding the dire warnings he was given early this year about the potential deadly impact of the virus.

Our focus group is underway.

The debate started with a conversation over which leader was better equipped to handle the next stage of the Covid-19 pandemic, here's what resonated with voters.

Andrew Marsteller, undecided voter: “When Trump says we are almost done with Covid-19, that we’re around the corner, I don't believe him."

Lesley Batson, Biden voter: “Trump continues to spew incorrect info, which is dangerous. Biden is taking this seriously.”

Rom Solene, Trump voter: “I don’t think there would be any difference between their approaches moving forward. The federal government is very limited in its ability to mandate people to wear a mask.”

And thirty minutes in... how do voters think the debate is going so far?

Noel Brown, undecided voter: “This debate is a lot more controlled, a lot more polite and considerate. I’m talking about both candidates.”

Jessica Altobelli, Biden voter: "Trump is definitely being less bombastic and not yelling as much. But lying in a nicer tone is still lying."

Eliana Girard, Trump voter: "Trump is a lot more calm and collected, he is more direct."

We're watching tonight's debate with voters from battleground states -the places that will ultimately decide the election.

Join our voter panel or submit your questions on the US election.

Anthony Zurcher
BBC North America reporter

The mute button, or at least the threat of it, seems to be working. Early in the second presidential debate, both candidates have been more restrained. They 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 Donald Trump’s constant interruptions may have cost him support in subsequent opinion polls, the president has very visibly dialed down the volume.

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.

Image source, Reuters

Russia and Iran are both working to influence the election, moderator Kirsten Welker says, asking what Biden and Trump plan to do about the claim from US intelligence officials that was announced yesterday.

"Any country that interferes in American elections will pay a price," begins Biden, saying it has been his clear position throughout his political career.

"They are interfering with American sovereignty. That's what's going on right now."

Russia, Biden says, would prefer Trump because "They know I know them. And they know me."

We’re now onto the next topic, which is US national security.

The debate is likely to turn fierce, as each of them declare that the other has a conflict of interest preventing them from safely protecting the country.

Trump claims that Biden’s son, Hunter, had been selling access to the White House while his dad was vice-president. There’s little evidence for the claim, which Trump has begun touting in recent weeks.

Meanwhile, Democrats say that Trump’s personal debts, to persons unknown, represent a major conflict of interest.

Reporting this week by the New York Times, indicating that Trump has a Chinese bank account and may have paid more taxes to China than the US in the past two decades, will probably be mentioned by Biden.

He may also bring up the fact that countless former US national security officials, including many Republicans, have denounced Trump as a threat to national security.

Read more:

Trump taxes 'a national security issue'

Image source, Getty Images

Image source, Getty Images

"We're learning to live with [the virus]," Trump says, "We can't lock ourselves up in a basement like Joe does...people can't do that."

He says he learned a lot from having caught the virus.

"Ninety-nine point nine of young people recover, 99% of people recover. We have to recover," Trump says. Experts have cautioned that the virus' 1% mortality rate scaled across the US population could mean millions dead.

Biden hits back: "People are learning to die with it."

Speaking to the people at home, he says people like you will have an empty seat at the kitchen table. "Learning to live with it? Come on. We're dying with it."

He adds that Trump doesn't take responsibility for the crisis.

Trump says he does, but then quickly blames China. "They didn't keep it from coming out to the world," the president says.

Chelsea Bailey
Digital producer, BBC News, Washington DC

Image source, Getty Images

President Trump has promised a vaccine against Covid-19 will be available "very soon" - at times even hinting that one could be approved before the election.

It’s true scientists are moving at unprecedented speeds to create a vaccine fo coronavirus, condensing a process that normally takes years into a matter of months.

But with just over half of Americans, external saying they’d take the jab if one were available, simply making the vaccine could be the first of many challenges.

"It’s going to be the biggest vaccination effort ever attempted," Dr Kelly Moore, who helped lead US vaccination efforts during the 2009 Swine Flu pandemic, told me.

Dr Moore says the Covid vaccine will likely require two jabs (what’s called a prime and a boost), and will have to be stored at incredibly low temperatures in specialised deep freezers. On top of that, there are questions over how much the vaccine will cost and who should get it first.

All of that means even if a vaccine becomes available in the near future, it could be months before most Americans can go to their local pharmacy to get one.

As the candidates duel over the pandemic on stage, let's turn for a moment to Glenn and Matt: two elderly Covid survivours who, like Trump, were hospitalised due to the virus.

But the two men have very different recovery experiences to the president's.

And while both are Republicans, Glenn and Matt have differing views on Trump.

The septuagenarians share how they recovered after weeks in hospital, and their thoughts on the president's illness and the state of the US pandemic response.

Video by Alexandra Ostasiewicz and Joaquim Moreira Salles

Tara McKelvey
BBC News, Washington

Trump appeared on stage mask-less. Biden wore one as he stepped onto the stage and then peeled his off. It is a public health matter – and also a political gesture. Most Republicans believe the US has controlled the outbreak of infection as best it could, according to Pew. Most Democrats do not.

Their attitudes are also reflected in how they feel about masks: conservatives such as those I’ve met in Kansas say each person should decide on their own whether or not to wear a mask, and that things are going to get better.

By appearing without a mask and speaking with confidence about his own recovery, Trump was trying to show he has the nation – and the rate of infection – under control.

Image source, Reuters

Now it's Biden's turn. He starts off by saying there's an expectation that the US will see another 200,000 deaths by the end of the year.

"If we just wore these masks," he says, holding up his own, "we could save 100,000 lives. And we're in a circumstance where the president thus far has no plan, no comprehensive plan."

The Biden plan then is making sure everyone is encouraged to wear masks, make sure there's rapid testing, set up national strategies to open up schools and businesses. He also points out that one of the best medical journals in the world recently decried the president's response as "absolutely tragic".

And to sum up Biden: "I will take care of this, I will end this, I will make sure we have a plan."

Image source, Reuters

The topic of Covid comes as there are over 8.4 million US cases and 222,000 deaths.

And President Trump gets the first question of the evening.

Since the last debate earlier this month, 16,000 Americans have died from Covid, Welker says. How would Trump lead in the next stage of the crisis?

He says spikes across the nation are "now gone", and "spikes and surges in other places they will soon be gone".

"We have a vaccine...it's going to be announced in weeks," Trump says, adding that the military will distribute it. He emphasises that the pandemic is a global problem.

"I can tell you from personal experience...I had it, I got better."

More on a potential virus vaccine here, and on Trump's medical experience here.

To sum up: Covid's going away, says Trump.

Angelica Casas
Video journalist, BBC News

In the last couple of months, I’ve covered how Covid-19 is affecting American families. For those who have lost loved ones to the virus, the personal tragedies are extreme, so the conversations I have with them are rarely political.

That changed when President Donald Trump got the virus. The stakes became higher for people like Rita Marquez-Mendoza, who lost her daughter and son-in-law to the virus. The couple left behind two teenage boys, aged 12 and 14.

“I don't blame anybody, but I do think that our leaders should have been more responsible, because they would have saved a lot of lives. A lot of us wouldn't have to sit at the dinner table missing one family member, and in our case, we're missing two family members.”

“That is very hard to go through, we don't know if we're ever going to be okay.”