The 90-minute debate quickly descended into chaos after Trump began to interrupt both Biden and the moderator, Fox News' Chris Wallace. The night didn't get much calmer from there.
Read highlights from Tuesday's debate below:
Trump tries to tie Biden to the Green New Deal, which he does not support
The candidates went back and forth over their climate positions (including where they stand on farting cows), during which Trump tried to paint Biden as beholden to the left wing of the Democratic Party, which supports an ambitious plan to tackle climate change known as the Green New Deal.
"That is not my plan. The Green New Deal is not my plan," Biden said.
"Oh, you don't? Well, that's a big statement," Trump said in a mocking voice.
Biden has proposed his own plan for economic reinvestment, which would create "10 million clean energy jobs," according to his campaign website, with a focus on renewable energy, small nuclear reactors and grid energy storage, among other initiatives.
The Biden plan adopts many of the same pillars of the Green New Deal but omits some of the more controversial elements, such as "Medicare for All," a federal jobs guarantee and a strict zeroing carbon emissions mandate.
Harris on family talk
Fact-check: Biden says violent crime fell under Obama, rose under Trump
Biden said: "Violent crime went down 17 percent, 15 percent in our administration. It's gone up on his watch."
Biden's attack is half-true. Asked about this claim, the Biden campaign pointed to a FactCheck.org review of FBI violent crime data during the Obama administration, which found that the violent crime rate fell by nearly 16 percent when adjusted for population. While that number appears to check out, his attack on Trump is unfounded: While homicide has been on the rise, violent crime has remained largely flat under the Trump administration.
'I don't know Beau': Trump dismisses Biden’s dead son, pivots to attacks on Hunter
Biden referred to a recent Atlantic story that reported that Trump had disparaged American service members, touching on his own son's service.
"He was not a loser. He was a patriot, and the people left behind there are heroes," Biden said of service members, including Beau Biden, his son who died in 2015 from cancer and served in Iraq.
"I don't know Beau," Trump said, dismissing the reference. He then pivoted to a mention of Biden's living son, Hunter, describing the younger Biden as an addict who had been dishonorably ejected from the military. "I know Hunter. Hunter got thrown out of the military. ... He was dishonorably discharged."
"That's not true," Biden interjected.
"For cocaine use," Trump responded, adding one of his repeated unproven claims that Hunter Biden's global business dealings amount to graft made possible by his father's status. "And he didn't have a job until you became vice president."
Hunter Biden was discharged from the Navy Reserve in 2014 after having tested positive for cocaine. Hunter Biden, his father said on the debate stage, also underwent treatment, overcoming addiction, a problem with which millions of Americans have struggled.
"I'm proud of my son," he said.
Beau Biden, a former attorney general of Delaware, died of cancer in 2015. Neither Trump nor his sons have served in the military. Both Eric Trump and Donald Trump Jr. have worked the bulk of their adult lives for Trump companies, like their father.
Analysis: Relying on white supremacist votes
It shouldn't be hard to condemn white supremacists. For Trump, though, it appears to be bad politics.
Asked to reject people so motivated by racism that they form groups devoted to it, Trump failed to do so. He seemed like he might do it.
"Stand back and stand by," he said after asking whom he was supposed to condemn. But instead of attacking white supremacists, he launched a rhetorical assault on "antifa." Antifa is not a white supremacist group.
The moment recalls Trump's refusal to denounce Ku Klux Klan leader David Duke during the 2016 campaign and his determination that there were "very fine people" on both sides of a white supremacist demonstration in Charlottesville, Virginia, in 2017.
Fact-check: Did Biden call Black Americans 'superpredators'?
"Look at the crime bill, 1994, where you called them 'superpredators,' African Americans are 'superpredators,'" Trump said. "And they've never forgotten that."
This is mostly false. It was Hillary Clinton, then the first lady, who used the word "superpredator" to advocate for the 1994 crime bill that Biden co-wrote more than 30 years ago. Biden did warn of "predators" in a floor speech in support of his bill, however.
Fact-check: Biden says Trump 'paid a total of $750 in taxes'
Biden, during a prolonged exchange over the amount of federal taxes Trump has paid, said, "This guy paid a total of $750 in taxes."
Trump retorted by saying, "I've paid millions of dollars in taxes, millions of dollars of income tax."
Biden's claim accurately reflects new reporting by The New York Times for 2016 and 2017.
Trump's federal income tax bill was just $750 the year he won the presidency, The Times reported after obtaining and reviewing more than two decades of the president's tax information. During his first year in office, his bill remained $750. The information doesn't include his returns from 2018 and 2019.
According to The Times, Trump had paid no income taxes at all in 10 of the 15 years before 2016, because he reported losing much more money than he made during that time. NBC News hasn't seen or verified any of the documents reported by The Times.
Fact-check: Does Trump support cutting police funding?
"His budget calls for a $400 million cut in local law enforcement assistance," Biden said, reiterating his own opposition to defunding the police.
That is mostly true, although Biden actually undercounts the proposed cuts. While Trump has opposed calls from some Democrats to reduce police funding in response to the deaths of George Floyd and other Black Americans over the summer, the Trump administration's budget proposal does, indeed, call for big cuts for several police programs.
In the Justice Department's budget plan for fiscal year 2021, the Trump administration requested $1.51 billion for over 50 programs funding state and local law enforcement. That number would cut about $515 million from previous fiscal years, in part by slashing budgets for a number of Obama-era programs, including initiatives that provided body cameras for police officers.
Trump portrays Biden as both too tough and too weak on crime
During an exchange on racism in America, Trump essentially argued that Biden was too tough on crime and is too weak on crime.
First, Trump condemned Biden for authoring the 1994 crime bill while, in almost the same breath, saying Biden wouldn't even say the words "law enforcement."
Biden later said he stands for law and order if it is applied equally regardless of race or creed.
Trump balks at denouncing white supremacy
In another heated exchange, Trump declined to denounce the far right and white supremacists and told the Proud Boys — a violent, far-right group — to "stand back and stand by."
Trump instead tried to pivot to antifa's being a more serious problem. Biden pointed out that the FBI has said the far right is the biggest threat to the U.S. in terms of domestic violence.
His own FBI director said this month that antifa is an ideology, not a group.