The outcome, which could be known overnight but may take days, will have momentous consequences, either making Harris the first woman in the world's most powerful job or handing a historic comeback to Trump and his right-wing "America First" agenda.
Millions of Americans formed long lines across the country to cast their vote, with polls already closing in Georgia and North Carolina, two of the crucial battleground states expected to tip the balance in the neck-and-neck race.
There were no surprises in the initial results. Republican former president Trump won strongholds Indiana, Kentucky and West Virginia, and Democratic vice president Harris took more liberal Vermont.
But in a stark reminder of the tension, and fears of outright violence, around the election, officials said 32 bomb threats were called into polling locations around Georgia.
In five stations, the threat required temporarily suspending voting while police checked for explosives, Fulton County police chief said.
The FBI and local authorities said the threats appeared to originate in Russia, which is accused by Washington of trying to meddle in the election.
In a possible preview of other election challenges, Trump took to social media to say there is "talk about massive cheating" in Philadelphia, the Democratic stronghold of crucial state Pennsylvania.
City Commissioner Seth Bluestein, a Republican, said there was "absolutely no truth" to the charge.
'Big victory'
Trump added as the first results came in that "we're going to have a big victory tonight."
The billionaire has still refused to accept his 2020 loss to Joe Biden, after which his supporters attacked the US Capitol.
There are fears of fresh violence if Trump loses and numerous buildings in central Washington were boarded up on Tuesday while barriers were erected around the White House.
Polls for weeks have shown a razor-thin race between Harris and Trump, who at 78 would be the oldest ever president at the time of inauguration, the first felon president, and only the second in history to serve non-consecutive terms.
All eyes will be on the other swing states, with polls due to close in Pennsylvania, the biggest prize, at 8:00 pm, in Arizona, Michigan and Wisconsin at 9:00 pm and in Nevada at 10:00 pm.
The Harris campaign reported strong turnout in the Democratic stronghold of Philadelphia, including among Puerto Ricans, who were disparaged by a comedian at a Trump rally a week earlier.
Harris, 60, would also be only the second Black and first person of South Asian descent to be president.
She made a late, dramatic entrance into the race when Biden dropped out in July, while Trump, twice impeached while president, has since ridden out two assassination attempts and a criminal conviction.
After crisscrossing the country over the weekend, Harris returned to Washington where she spent the day calling into radio stations and taking a few calls personally at a phone bank for voters.
"We've got to get it done. Today is voting day, and people need to get out and be active," Harris told Atlanta station WVEE-FM.
Trump voted in Florida near his Mar-a-Lago residence, saying he felt "very confident" and that he wanted to be "very inclusive."
Right-wing tech tycoon Elon Musk, who has backed Trump, said he planned to spend election night with the former president.
Long voter lines
Casting a ballot in Arizona, Trump backer Camille Kroskey, 62, said she was voting in person due to concerns about voting fraud.
"I want to make sure I drop my ballot where it's going to actually land somewhere," she told AFP.
In Pennsylvania, Harris voter Marchelle Beason, 46, said the lines were "way, way, way more" than in the last election.
Trump has vowed an unprecedented deportation campaign of millions of undocumented immigrants, in a campaign full of dark rhetoric.
Harris has hammered home her opposition to Trump-backed abortion bans in multiple states, a vote-winning position with crucial women voters.
The election is meanwhile being watched closely around the world including in the war zones of Ukraine and the Middle East, anxious to see how the next Oval Office occupant deals with the conflicts.
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