Hillary Clinton and Donald Trump have been criss-crossing America in a final push for votes before election day.
Both have held rallies in the battleground states of North Carolina, Pennsylvania and Michigan.
Mrs Clinton urged voters to back a “hopeful, inclusive, big-hearted America” while Mr Trump told supporters they had a “magnificent chance to beat the corrupt system”.
Polls give Democrat Mrs Clinton a four-point lead over Republican Mr Trump.
A record number of Americans – more than 46 million – have voted early by post or at polling stations.
There are signs of a high turnout among Hispanic voters, which is believed to favour Mrs Clinton.
It was after midnight when the rivals held the final rallies of their campaigns – Mr Trump in Grand Rapids, Michigan, and Mrs Clinton in Raleigh, North Carolina.
“Today the American working class is going to strike back, finally,” said Mr Trump, pledging to reverse job losses.
Earlier, in New Hampshire, he told supporters: “We are just one day away from the change you’ve been waiting for all your life.
“Together we will make America wealthy again, we will make America strong again, we will make America safe again and we will make America great again.”
Mrs Clinton told her audience that they did not “have to accept a dark and divisive vision of America”.
She looked forward to “a fairer, stronger, better America. An America where we build bridges, not walls. And where we prove conclusively that love trumps hate”.
Election day follows a bitter campaign during which the candidates have traded insults and become mired in a series of scandals.
At a star-studded event in Philadelphia, Pennsylvania, Mrs Clinton was joined on stage by celebrities Bruce Springsteen and Jon Bon Jovi as well as her husband Bill, President Obama and his wife Michelle.
Earlier Mrs Clinton said in a radio interview that if she won she would call Mr Trump and hoped he would play a “constructive role” in helping to bring the country together.
The businessman described Mrs Clinton as the “most corrupt person ever to seek the presidency”, referring to an FBI investigation into Mrs Clinton’s use of a private email server while she was serving as secretary of state between 2009 and 2013.
On Sunday Mrs Clinton’s campaign received a boost when the FBI said newly discovered emails sent by an aide showed no evidence of criminality.
Election day voting began just after midnight in the small New Hampshire village of Dixville Notch in New Hampshire, where seven votes were cast – four for Mrs Clinton and two for Mr Trump.
Results are expected some time after 23:00 EST (04:00 GMT on Wednesday) once voting ends on the West Coast. State projections will not be available until polling ends – in most states between 19:00 EST (24:00 GMT) and 20:00 EST (01:00 GMT).
Americans are also voting for Congress. All of the House of Representatives – currently Republican controlled – is up for grabs, and a third of seats in the Senate, which is also in Republican hands.
Meanwhile Mr Trump’s campaign manager Kellyanne Conway sought to allay international anxiety about the Republican candidate in a BBC interview on Monday.
She said criticism from abroad “does not reflect why Donald Trump is running and who he would be on the global stage”.
French President Francois Hollande has said the billionaire made him “want to retch”.
It follows a series of sex assault allegations made against Mr Trump, which he denies, and the emergence of a recording of him making obscene remarks about women.
Mr Trump has also been accused of stoking xenophobic sentiment after vowing to ban Muslims from entering the US, describing Mexicans as “rapists” and saying he would build a wall along the US southern border to stop illegal immigration.
BBC
