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To better understand the US vote, read our simple guide to the US election here. And check out our coverage of swing states like North Carolina and Georgia.

And with five days left, read more about what the polls say here.

We’ll soon be closing this live page. Here are the top updates from today:

• Both Donald Trump and Kamala Harris campaigned in the western part of the US, crisscrossing the key swing states of Arizona and Nevada.
• Harris topped her night with a performance by Jennifer Lopez in Las Vegas, as she seeks to connect with Latino voters in the final days of the race.
• Trump, meanwhile, appeared with far-right media personality Tucker Carlson in Phoenix, Arizona.
• More than 65 million people have cast their ballots in the race, as of October 31 at 11 pm EST.

Harris, the Democratic presidential candidate, has been pushing her candidacy as representative of a “new generation of leadership” – and as she closed her remarks at her star-studded Las Vegas event, she made an appeal to young voters to support her.

“I see the promise of America in all the young leaders who are here in our voting for the first time,” she told the crowd.

Her voice rising with emotion, she spoke to the immediacy of the issues facing the younger generation – and the activism she sees in their ranks.

“I love Gen Z. I love you. And here’s what I love about our young leaders. You guys are rightly impatient. You are rightly impatient for change. You are young leaders who are determined to live free from gun violence, to take on the climate crisis. You intend to shape the world you inherit.

“I love that about you because, for you, none of these issues is theoretical. It’s not political. This is your lived experience.”

Harris left the stage to her campaign anthem, Beyonce’s song Freedom, offering hugs to the night’s performers and her husband, Doug Emhoff.

Jumping from subject to subject, with little mind for Carlson’s questions, Trump meandered through his appearance in Glendale, Arizona.

He spent time espousing the importance of firing people in his administration, saying he would make sure he appointed better people if he is re-elected. It was an apparent response to the deluge of former officials who have come out against Trump.

He also took time to deride former National Security Adviser John Bolton, as well as Republican Liz Cheney, who has been campaigning with Harris. Trump called Cheney the “repulsive little daughter” of former Vice President Dick Cheney.

In addition, Trump made baseless accusations against the congressional panel that investigated the riot at the US Capitol on January 6, 2021. He dubbed the proceedings a “cover-up”.

In the often hard-to-follow statements, Trump further attacked prosecutors in Georgia and New York who have indicted him.

Harris, the Democratic nominee for the presidency, has campaigned heavily on the question of abortion access, something her Republican opponent Trump helped to restrict.

But during her speech in Las Vegas, Nevada, she also called on voters to vote “yes” on a ballot initiative that would enshrine abortion rights in the state constitution this November.

“It is a fight for freedom. Like the fundamental freedom of a woman to make decisions about her own body and not have her government tell her what to do,” she said.

She also went on attack against Trump, pointing out his role in the overturning of the 1973 Supreme Court decision, Roe v Wade, which previously upheld a federal right to abortion.

“We all remember how we got here. When Donald Trump was president, he hand-selected three members of the United States Supreme Court with the intention that they would undo the protections of Roe v Wade. They did as he intended,” she explained.

When she cited a quote Trump made about protecting women “whether they like it or not”, the crowd broke into chants of “Lock him up! Lock him up!”.

It was a phrase Trump’s supporters previously used against his opponents – and that Democrats have since appropriated.

Harris smiled and responded, “I hear you, but you know what? The courts are going to handle that. The courts will handle that. We’ll handle November.”

Trump is the first president to face criminal charges in US history.

He may have been appearing at multiple rallies across New Mexico, Nevada and Arizona.

But multiple versions of Donald Trump were also seen marching in New York City’s 51st annual Village Halloween Parade.

Take a look at how some parade participants paid homage to – or mocked – the Republican presidential candidate.

“We have work to do. But we like hard work. Hard work is good work. Hard work is joyful work. And make no mistake: We will win.”

Following a speech from the Puerto Rican American singer Jennifer Lopez, Harris herself took the stage to rally voters in the swing state of Nevada. She quickly reprised her usual theme of unity over division.

“We all know we have an opportunity in this election to turn the page on a decade of Donald Trump, trying to keep us divided and afraid of each other. We’re done with that. We’re done. We’re exhausted with it,” she told the Las Vegas crowd.

“And we know that is who he is. That is who he is. But Las Vegas, that is not who we are. That is not who we are. And it is time for a new generation of leadership in America. And I am ready to offer that leadership as the next president of the United States.”

In a meandering answer to Carlson, Trump said the reaction to his portrayal of political opponents as the “enemy within” was overblown.

“But you know, we do have an enemy from within. We have some very bad people, and those people are also very dangerous,” he said, without specifying.

“They would like to take down our country …They’re the greatest con artists,” he added. “These are sick puppies.”

Speaking in Las Vegas, Nevada, the actress and singer gave an impassioned speech. Pointing to Harris’s middle-class upbringing, Lopez said, “She gets it.”

“Kamala will fight for our freedom: the freedom of immigrants and immigrant families to chase the American dream; the freedom of workers to receive education, food and life’s essentials; and the freedom of women to choose what we do with our bodies,” she said.

Lopez added that Trump’s Madison Square Garden rally, at which Puerto Rico was referred to as a “floating island of garbage”, hurt not just Puerto Ricans.

“It was every Latino in this country. It was humanity and anyone of decent character,” she said.

She added: “I like Hollywood endings. I like when the good guy, or in this case the good girl, wins.”

Taking the stage with Carlson in Phoenix, Arizona, Trump said he would not have run if not for the 2020 election.

“We did much better in the second election,” Trump said.

“Bad things happened. Bad, bad, bad things happened,” he said, invoking his unfounded claims that the 2020 vote was marred by fraud. “We know how well we did.”

Trump appeared to again lay the groundwork for challenging this year’s vote.

“We’re doing very well. I think we’re leading by a lot. And if we can keep them, we can keep that cheating down – because they’re a bunch of cheats – if we can keep that cheating down, we’re gonna have a tremendous victory,” Trump said.

As he continued, Trump claimed Democrats are “trying to sign people up who don’t know what country they’re in”.

“That’s the moment little boys dream about.”

That’s how former Fox News host Tucker Carlson described the July assassination attempt against former President Trump, describing it as the kind of experience men use to “prove they are men”.

As Trump himself prepared to take the stage, Carlson launched into a defence of masculine stereotypes, telling the audience: “Masculinity is still an indispensable thing.”

He also mocked US Representative Alexandria Ocasio Cortez, known as AOC, for comments in praise of Harris’s husband, Doug Emhoff.

“AOC raised the question of what a real man looks like. Let me just tell you my view of what a real man looks like,” Carlson said, sketching a vision of strength tested by violence.

“A real man is a cheerful man. And he’s cheerful because he’s brave. Brave people have hope. Because they have a mission and they’re strong inside. And they know because they are living for something greater than themselves. That even if they die, they don’t die. The mission lives on.”

“They are bright, bright-eyed, cheerful, energetic and in command. And that is exactly what Trump has proven to be, including on the day he was shot in the face.”

The Republican Party, under Trump, has been criticised for purveying an image of masculinity that is dominant and violence-fuelled, playing into long-held Western stereotypes about gender.

Harris herself criticised Trump earlier in the day for saying he would “protect” women – whether they “like it or not”.

Of course, there is no crystal ball to tell us who will prevail on November 5.

The polls, as much as they can be trusted, show Harris and Trump running neck and neck in what many observers believe could be the closest election in decades.

Even so, the performance of US stocks has an uncanny track record of predicting the outcome of presidential elections.

Since 1928, the S&P 500 – which tracks the performance of 500 of the largest firms listed in the US – has pointed to the winner in 20 out of 24 elections, according to an analysis by financial services company LPL Financial.

Read more in our story here.

In the Phoenix suburb of Glendale, Arizona, former Fox News personality Tucker Carlson warmed up the crowds for Trump.

“I’m really grateful to be here. I never thought that I would be speaking at a rally for Donald Trump,” Carlson said.

“This is the fourth time I’ve done it. And it has felt not only like an honour and a privilege every time, but it has felt really natural. I’m sort of surprised. I was in journalism for 33 years.”

He proceeded to mine a theme often repeated at Trump rallies: slamming the media.

“It’s nothing to brag about,” Carlson said of his career at Fox News. “Trust me. And I honestly feel like saying I was young and I needed the money. It’s almost like when the naughty pictures of you emerge, and you’re like, ‘Ah, that was the old me’.”

Carlson was dismissed from Fox News in April 2023. A defamation lawsuit that same year revealed text exchanges where Carlson said of Trump: “I hate him passionately.”

That clashed with his public persona, which has been in firm support of Trump.

One of the first remarks Harris made in her one and only presidential debate against Trump was about an issue that frequently appears at the top of voters’ concerns: housing.

“We know that we have a shortage of homes and housing. And the cost of housing is too expensive for far too many people,” Harris said.

Housing is the second most common economic concern for American families in the lead-up to the presidential elections, only trailing inflation, according to a recent Gallup poll.

But what is Harris planning to do to tackle the issue? And where does her Republican rival Trump stand?

Find out in our analysis here.

After a comedian at Trump’s Madison Square Garden rally called Puerto Rico a “floating island of garbage”, prominent artists with ties to the island came out strongly against the remarks – and offered their support to Trump’s rival, Harris.

Among them was Jenny from the Block herself: singer and actor Jennifer Lopez, a New York native and proud member of the Puerto Rican diaspora.

Lopez is set to headline tonight’s Harris rally in Las Vegas – but it is not her first foray into politics.

During the 2020 presidential election cycle, Lopez headlined the Super Bowl halftime show, a key moment in one of the most watched sporting events in US culture.

At the time, Trump was president and facing severe criticism for his immigration policies, including a measure that separated parents and children who crossed the border irregularly.

Lopez appeared in the halftime show wrapped in a feathery Puerto Rican cape, and critics said her rendition of Bruce Springsteen’s hit song Born in the USA – as well as her daughter performing in a cage-like structure – were meant to be rebukes to the immigration measures at the time.

Later that year, she and her then-beau Alex Rodriguez endorsed Joe Biden in a campaign video.

“I’m here representing women and moms and Latinos and Americans,” she said in the video. She also offered a message in Spanish.

“La comunidad latina va a determinar lo que va a pasar en esta eleccione,” she explained at the time: The Latino community will determine what happens in this election.

The scion of a prominent family of Democratic politicians, Robert F Kennedy Jr has again taken the stage for Trump, this time during an event in Phoenix, Arizona.

His appearance comes after the Washington Post reported today that the former Democrat is poised to take on a significant role in the Trump administration, potentially overseeing heath and food safety.

Trump referenced that earlier today while speaking in Nevada, saying Kennedy would be taking on “health and women’s health”.

Kennedy, however, has led a crusade against vaccines, including during the COVID-19 pandemic.

Speaking to a crowd in Arizona, he said: “It was inconceivable to me that I would ever leave the Democratic Party. But I didn’t leave the Democratic Party. The Democratic Party left me.”

Detroit City Clerk Janice Winfrey has said security has been heightened ahead of November’s general election, and there will be a heavy police presence at the Huntington Place convention centre where ballots will be counted.

Michigan is a key swing state in the race, and all eyes will be on the state on election night.

Winfrey said her office has been working with local police agencies, Michigan’s attorney general’s office and the Justice Department on what she calls a “comprehensive security plan throughout this week and the days moving forward”.

Detroit has about 524,000 registered voters, and it is anticipated that voter turnout for this election will be somewhere between 51 percent and 55 percent, Winfrey said.

Turnout in the city in the 2020 general election was 51 percent.

Thousands of women are expected to visit the grave of Susan B Anthony after casting their ballots, in a tribute to the well-known suffragist.

In 2016, when Hillary Clinton was the Democratic candidate, an estimated 10,000 people passed through the Mount Hope Cemetery in Rochester, New York, on Election Day to cover Anthony’s headstone with “I Voted” stickers and flowers.

With another woman – Kamala Harris – on the presidential ballot, the crowds are expected to rival those numbers.

In 1872, Anthony defied the law by casting a vote in the presidential election, leading to a charge of “knowingly voting without having a lawful right to vote”.

She died 14 years before ratification of the 19th Amendment, which gave women the constitutional right to vote in 1920.

The Western part of the US boasts two prominent battlegrounds this election cycle: the neighbouring states of Arizona and Nevada.

To the south, Arizona has a more recent history as a swing state. One of the last states to join the US – just before Alaska and Hawaii – Arizona had been a Republican stronghold for much of the last 70 years.

Since 1952, starting with candidate Dwight Eisenhower, Arizona has consistently voted Republican, aside from a blip in 1992 when it flipped for Democrat Bill Clinton.

But that changed in 2020. Like the southern state of Georgia, Arizona went from backing Trump in 2016 to seeing him defeated within state lines in 2020, tilting towards Democrat Joe Biden instead.

Nevada, the so-called Silver State, has a longer history of flipping. It voted for Clinton twice in the 1990s, before embarking on another streak of red in the 2000s. Then it flipped back with the ascent of Democrat Barack Obama in 2008, and it has voted Democratic in presidential races ever since.

But the margins have been tight. Biden won over Trump in 2020 by just 33,596 votes.

Pollsters say the state is especially difficult to call because the number of independent voters greatly outweighs the number of registered Democrats and Republicans.