Mr Biden, a former vice-president, has a healthy national lead in the latest polls ahead of Tuesday’s election.
But his advantage is narrower in key states which could decide the result.
More than 90 million people have already cast their ballots in early voting, putting the country on course for its highest turnout in a century.
In the US election, voters decide state-level contests rather than an overall single national one.
To be elected US president, a candidate must win at least 270 votes in what’s called the electoral college. Each US state gets a certain number of votes partly based on its population and there are a total of 538 up for grabs.
This system explain why it’s possible for a candidate to win the most votes nationally – like Hillary Clinton did in 2016 – but still lose the election.
Tuesday’s vote comes amid the ongoing coronavirus pandemic. The US has recorded more cases and more deaths than any other country worldwide, reporting more than 81,000 new infections on Sunday alone.
Top virus expert Anthony Fauci has sharply criticised the Trump administration’s handling of the pandemic, drawing a rebuke from the White House on Sunday.
What are the two candidates concentrating on?
President Trump had a punishing schedule on Sunday, holding rallies in Iowa, Michigan, North Carolina and Georgia, and later in Florida.
In Michigan, Mr Trump boasted his leadership the state’s car manufacturing industry had been revived.
“The economy is now growing at the fastest rate ever recorded,” he claimed.
The US economy saw record-breaking 33% growth in the third financial quarter of this year, following a record 31% contraction in the second. But economists warn the damage inflicted by the pandemic – the biggest decline in the US economy in more than 80 years – could still take years to overcome.
At a later rally in Iowa, Mr Trump promised secure borders and more conservative judges in the courts.
Addressing Covid-19, he told supporters they had a choice between a “deadly Biden lockdown” or “a safe vaccine that ends the pandemic”.
Meanwhile, Mr Biden headed to Pennsylvania, his place of birth and another key state.
At a rally in Philadelphia, Mr Biden addressed the city’s black community, vowing to confront “systemic racism” in the US and attacking the president’s handling of the pandemic – something which has disproportionately affected African Americans.
“It’s almost criminal the way he’s handled it,” he said. “It’s a mass casualty event in the black community and it’s totally unnecessary.”
Mr Biden earlier courted Latino voters with a tweet in Spanish, speaking of the separation of migrant families at the border and Mr Trump’s “indifference” to the suffering of Puerto Rico after Hurricane Maria struck in 2017.
Mr Biden’s campaign said he would “fan out” to “all four corners” of Pennsylvania on Monday, joined by the pop stars Lady Gaga and John Legend. The Democratic challenger will also go to Ohio.
Meanwhile, Mr Trump will hold more rallies in North Carolina, Pennsylvania, Michigan and Wisconsin.
Are we going to get a result on election night as usual?
It can take several days for every vote to be counted after any US presidential election, but it’s usually pretty clear who the winner is by the early hours of the following morning.
In 2016, Donald Trump took to the stage in New York at about 03:00 local time to give his victory speech in front of a crowd of jubilant supporters.
But don’t set your alarm clocks just yet. Officials are already warning that we may have to wait longer – possibly days, even weeks – for the result this year because of the expected surge in postal ballots. The last time the result wasn’t clear within a few hours was in 2000, when the winner wasn’t confirmed until a Supreme Court ruling was made a month later.
Different states have different rules for how – and when – to count postal ballots, meaning there will be large gaps between them in terms of reporting results. In some states it will take weeks to get complete results.
On Sunday, a report by news site Axios said Mr Trump would declare victory on Tuesday night if it looked as if he was ahead.
Mr Trump denied the report, but said that counting ballots after election day was a “terrible thing”.
Meanwhile, Mr Biden vowed to stop the Trump “stealing” the election.
How do the candidates differ in what they are offering?
The two rivals have radically different policies on several key issues.
On the coronavirus outbreak, Mr Trump set up a task force in January which he says has now shifted its focus to “safety and opening up our country”. The president is also prioritising the speedy development of Covid treatments and vaccines, directing $10bn towards such projects.
Mr Biden wants to set up a national contact-tracing programme, establish at least 10 testing centres in every state, and provide free coronavirus testing to all. He supports a nationwide mask mandate, which would require face coverings to be worn on federal property.
On climate change, Mr Trump, being a sceptic, wants to expand non-renewable energy, and he has committed to withdrawing from the Paris Climate Accord.
Mr Biden says he would immediately re-join the Paris deal, and he also wants the US to reach net zero emissions by 2050.
On the economy, Mr Trump has pledged to create 10 million jobs in 10 months, as well as one million new small businesses. He wants to deliver an income tax cut, and provide companies with tax credits to incentivise them to keep jobs in the US.
Mr Biden wants to raise taxes for high earners to pay for investment in public services, but says the increase will only impact those earning over $400,000 a year. He supports raising the federal minimum wage to $15.