Hillary Clinton and Donald Trump have cast their ballots in the US election, with the latter saying it will be a "tremendous waste of time" if he misses out on the White House.

Millions of Americans are going to the polls to elect their 45th president at the end of an acrimonious and wildly unpredictable campaign that has divided the nation.

America will either have its first female commander-in-chief in Mrs Clinton, or choose billionaire tycoon Mr Trump, a flamboyant former reality TV star who has rocked US politics.

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As the clock ticked towards polls closing, Mr Trump renewed his familiar refrain about the "rigged" election system.


Image: Hillary Clinton, with husband Bill, greets supporters after casting her vote

When asked if he would accept the results, he sounded coy, telling Fox News: "We're going to see how things play out. I want to see everything honest."

Mrs Clinton was out early on Tuesday morning, greeting supporters waiting outside her polling station as she and husband Bill cast their ballot in their home town of Chappaqua, New York.

She said it was "the most humbling feeling" to vote "because so many people are counting on the outcome of this election."

Mr Trump, who arrived at a New York City polling station earlier, expressed confidence he would "win lots of states".

He told Fox News: "If I don't win, I will consider it a tremendous waste of time, energy and money."

Image: Donald Trump casts his ballot

Heavily armed police guarded Mr Trump as he voted at Public School 59 in Manhattan, a short distance from Trump Tower.

Hundreds of people watched outside as the Republican was greeted by a mixture of boos and cries of "Donald, Donald".

Mr Trump - who was accompanied by his wife Melania, daughter Ivanka and son-in-law Jared - said it was a "great honour, a tremendous honour" to be casting his ballot.

He said his final message to voters was: "Make America great again. That's all it is. That's what it's all about."

Image: Phoenix, Arizona: Hillary Clinton supporter Jorge Mendez wears a dress and Hillary Clinton mask while holding a doll of Donald Trump after casting his vote Image: Concord, New Hampshire: Voters fill out their ballots at the Green Street Community Centre Image: Chappaqua, New York: Hillary Clinton is surrounded as she votes at Douglas Grafflin Elementary School. Image: New York: Donald Trump punches the air after casting his vote Image: Tallahassee, Florida: Margo Layerd casts her vote at a precinct at Lafayette Park with her 13-year-old son Jonah by her side Image: New York: School cafeteria workers hope to capture a picture of Donald Trump after he casts his vote at the Beckman Hill International School Image: Florissant, Missouri: Voters wait in line to cast their ballots at Hazelwood Central High School. Long queues were reported at polling stations across Amer Image: Harlem, New York. A voter chats with an election worker at Samuels Community Centre Image: Arlington, Virginia: An unidentified toddler watches his mother fill out a paper ballot Image: Counterterrorism police patrol near Trump Tower, New York. City. There is a heavy police presence in the city following intelligence of a possible al Qaeda Image: New York: A worker prepares the teleprompter in the election night room for Donald Trump. Both candidates will be in New York on election night Image: New York: Microphones on stage at the Javits Centre where Hillary Clinton will give her election night address Image: Voters at a polling station on a basketball court in Greenville, North Carolina Image: People watch voting results at Mrs Clinton's election night event at the Jacob K. Javits Convention Center /

Long queues have been reported at polling stations across the country, with a high turnout expected.

Most polls show Mrs Clinton in the lead, with US election analyst Todd Donovan telling Sky News: "Objectively it's Clinton's election to lose."

According to a poll released before voting began, Mrs Clinton has about a 90% chance of defeating Mr Trump.

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The Reuters/Ipsos States of the Nation survey found Ms Clinton was leading Mr Trump 45% to 42% in the popular vote, and was on track to win 303 votes in the Electoral College to her rival's 235, clearing the 270 needed for victory.

The RealClear Politics poll of polls also gives the Democratic nominee a lead of more than 3% over her Republican rival.

The Democratic candidate is banking in part on a high turnout - particularly among Mr Obama's young, diverse coalition of voters.

In a possible good sign for her, roughly half the states with advance voting have reported record turnout, including Florida and Nevada, which have booming Hispanic populations.

How does the Electoral College work?

In other developments:

:: Donald Trump Jr told MSNBC his father would concede defeat if he loses, provided the result is "legit and fair".

:: President Barack Obama said "progress is on the ballot", as he urged Americans to vote. He wrote on Twitter: "Go vote - then make sure your friends, your family, and everyone you know votes too."

:: Mr Trump's second son Eric may have broken New York state law by tweeting a photo of his completed ballot. A law bans voters from showing marked election ballots to others, with a federal judge ruling last week this applies to social media posts.

:: Mr Trump's campaign sued the registrar of voters in Clark County, Nevada, over a polling place that had been allowed to remain open late last week to accommodate people who were queuing to vote. The lawsuit claimed the registrar violated state law, but a judge has rejected a request for an order to be issued in the case.

:: Election officials say problems with voting machines in southern Utah are forcing poll workers to use paper ballots, potentially affecting tens of thousands of voters.

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The election will be held under tight security, after authorities received intelligence of a possible pre-election al Qaeda attack.

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Both candidates held a last day of frantic campaigning to energise supporters and win over any undecided voters.

Flanked by ex-presidents, rock stars and family, the candidates blitzed through a handful of battleground states on Monday where the race will be largely decided.

The two candidates struck very different tones as they made their last appeal to the nation.

Clinton shoring up the 'blue' states

Mrs Clinton sounded optimistic, buoyed by FBI Director James Comey's announcement that he would not recommend criminal charges against her following a new email review.

She urged voters to embrace a "hopeful, inclusive, bighearted America," and was accompanied by Bill Clinton, President Barack Obama and First Lady Michelle Obama.

Bruce Springsteen and Jon Bon Jovi joined the rally, while in Manhattan, Madonna belted out some of her biggest hits in a surprise outdoor concert in support of Mrs Clinton.

Mr Trump, who sped through five rallies on Monday, kept up the aggressive approach that has carried him to the brink of the presidency.

He vowed to "beat the corrupt system," slammed Mrs Clinton as "the face of failure" and criticised the "crooked media".

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"You have one magnificent chance to beat the corrupt system and deliver justice. Do not let this opportunity slip away," he said.

Mr Trump reiterated the "America-first" message that has resonated across the nation with people who feel left behind by globalisation and disenfranchised by what they see as the Washington elite.

Control of Congress, key to any US president, is also at stake. All 435 seats in the House of Representatives are up for grabs as well as 34 in the Senate.

The Republicans enjoy a majority in both chambers, and they are considered to be most at risk of losing control of the Senate.

About a dozen states are also electing governors and several are deciding whether to legalise marijuana, either for recreational or medical use.

:: Sky News will bring you every twist and turn of the US election results - and we're the only UK news organisation which will bring you details of the official exit poll. Our special coverage starts at 10pm.

Read more:

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:: The states that will decide the outcome

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:: Power families: The Clinton and Trump clans

:: US election: Quirks, figures and fun facts