Mr Trump refused to participate in the second event, planned for October 15, after it was announced the event would be held virtually.
“I’m not going to do a virtual debate,” Mr Trump told Fox News, calling the decision “ridiculous” moments after the Commission on Presidential Debates announced the changes.
Looking to avoid the disruptions that marred the first meeting, organisers have announced that the October 22 debate will feature a mute button to allow each candidate to speak uninterrupted during their opening statements.
The Trump campaign voiced objections to the change, but said the president would still take part. It is one of Mr Trump’s last chances to reach a large prime-time audience before voting ends.
The coronavirus pandemic has drastically changed how the Republican and Democratic presidential campaigns are being fought this year, meaning the debates have taken on even more significance than in previous years.
Read more: Election 2020 polls
When, where and what time are the debates?
September 29, Ohio
The first presidential debate between Mr Trump and Mr Biden was a chaotic squabble between the two candidates.
The rivals ripped chunks out of each other on their records and issues such as the economy, coronavirus and racism.
Mr Trump was rebuked several times by Chris Wallace, the moderator, for speaking over his opponent. At one point, after incessant interruptions from the president, Mr Biden said: “Will you shut up, man?”
Read more: Who won the US election debate?
October 7, Utah
Trading barbs through plexiglass shields, Republican Mike Pence and Democrat Kamala Harris turned the only vice presidential debate of 2020 into a dissection of the Trump administration’s handling of the coronavirus pandemic, with Ms Harris labelling it “the greatest failure of any presidential administration”.
Mr Pence, who leads the president’s coronavirus task force, acknowledged that “our nation’s gone through a very challenging time this year”, yet vigorously defended the administration’s overall response to a pandemic that has killed 210,000 Americans.
They also went head-to-head on abortion, the Supreme Court and the environment.
The meeting was far more civil than the chaotic face-off between President Trump and Mr Biden.
Read more: Who won the vice-presidential debate?
October 15, Florida
The second debate was scrapped, leaving an October 22 event the final Trump-Biden showdown before election day on November 3.
The debate was to take the form of a town hall event, with Miami residents in the audience posing their own questions to the two candidates.
The candidates instead took place in separate town hall events on Oct 15.
Read more: Donald Trump vs Joe Biden policies
October 22, Tennessee
The final presidential debate will be at Belmont University in Nashville, Tennessee, on October 22 at 9pm ET (2am Oct 23 in the UK).
Mr Trump and Mr Biden will have their microphones turned off at Thursday’s presidential debate to enforce two minutes of uninterrupted speaking time for each candidate per topic after the first debate between rivals became a farce.
The 90-minute event, moderated by NBC News correspondent Kristen Welker, will also be divided into 15-minute segments on prepared topics.
How can I watch the debate in the UK?
Each debate will be streamed by all major US networks, including ABC, CBS, NBC, Fox News, CNN and MSNBC.
The Telegraph will be livestreaming the first debate – watch it above or on our YouTube channel here.
What do we know about the moderators?
The key details for the debates, as well as who moderates them, are decided by the non-partisan Commission on Presidential Debates.
Moderators can play an outsized role in how the candidates fare because they choose the questions, can push back on vague responses and dictate how many interruptions they allow.
Unlike in previous years, there is only one moderator in each debate as a way to limit the number of people on stage during the coronavirus pandemic.
The Trump campaign outlined its preferred moderators, including a number of Fox News hosts and conservative commentators, in a list that Rudy Giuliani sent to the commission, but none of the suggestions were selected.
The initial debate was overseen by Chris Wallace, a host from Mr Trump’s favourite network Fox News, but one of his toughest questioners at the network. Mr Wallace was criticised for losing control of the discussion and allowing Mr Trump to frequently speak over his opponent.
The second debate was due to be moderated by a journalist from the public service network C-SPAN, and the third by one from NBC.
The single vice-presidential debate was moderated by a USA Today newspaper journalist. How important the moderators can be has been shown repeatedly over the years. Their actions can help decide an election.
What happened in the town halls?
After the second presidential debate was cancelled, the two candidates appeared in separate live town halls that were broadcast at the same time.
Mr Trump dominated the headlines after he refused to denounce the QAnon conspiracy theory, which falsely claims the US government is controlled by a “deep state” cabal of anti-Trump Satanist paedophiles.
He said: “So, I know nothing about QAnon. I know very little. What I do hear about it, they are very strongly against paedophilia. I do agree with that.”
The president was questioned over his decision to retweet a false conspiracy theory, from a QAnon-linked Twitter account, suggesting that Navy Seals killed a body double of Osama bin Laden, and that the Obama administration covered it up. Mr Trump said he was just “putting it out there” and “people can decide for themselves”.
Mr Trump also denied that he was told in the Oval Office, by his national security adviser in January, that the coronavirus would be the biggest national security threat of his presidency.
In Philadelphia, Mr Biden said: “We’re in a situation where we have 210,000 plus people dead and what’s he doing? Nothing. He’s still not wearing masks.”
Mr Biden put on his mask when leaving the stage to be closer to questioners.