Shortly before Mr Trump's arrival, two topless female protesters were removed from the polling station. One could reportedly be heard shouting "Out of our polls, Trump!"   

Some more details of Mr Trump casting his vote: he turned up at a polling station on Manhattan's East Side accompanied by his wife Melania, daughter Ivanka and son-in-law Jared. 

"It's a great honour, a tremendous honour," he said, casting his ballot. Asked if he was still concerned about possible voter fraud, he said: "We're always concerned about that.''

"Make America great again," was the Republican's final appeal to voters. "That's all it is. That's what it's all about.''   

If you are just joining us, tens of millions of voters in the US are electing a new president after one of the bitterest contests in living memory. 

Hillary Clinton and Donald Trump have both cast their votes after a gruelling final push for votes. 

Long lines of voters are reported in some places but the process appears to be going smoothly.

We'll bring you the latest updates and analysis from our correspondents on the ground as well as curating coverage from across the web. 

Below is a selection of our essential US election reads to get up to speed on this historic day:

• All you need to know
• Who is ahead in the polls?
• Who is going to win?
• Full election coverage from the BBC
• Hour by hour guide to election night

Image source, Getty

The New York Times has published pictures of its post-election reports since 1852 (when Franklin Pierce became president, if you were wondering).

The paper's style has changed hugely down the years, from the six columns of dense text finally making way for a map (1896), what we would recognise as a headline (1916), a headshot of the new president (1932) and eventually colour photographs (2000).

Flick through the ages here, external.

We're willing to bet that tomorrow's winner will make the front page... not like in 1852 and 1856, when the NYT put its tentative election reports on page 4.

Image source, New York Times

Mr Trump cast his vote in New York city. Speaking earlier by phone to Fox News, he said: "I see so many hopes and so many dreams out there that didn't happen, that could have happened, with leadership, with proper leadership. And people are hurt so badly."

Image source, Getty

Donald Trump has just voted.

Few voters appear to be encountering problems so far, AP reports. Presidential elections usually include sporadic voting problems such as machines not working properly, the US news agency adds, noting that some technical hitches have been reported in Virginia and North Carolina.

Long queues of voters are being reported in places. These people were queuing in Washington DC.

Image source, AFP

Donald Trump's highly personalised use of Twitter may have been one of the more memorable features of the campaign but, in the end, the two candidates posted equal numbers of tweets, according to the social media analytics company Socialbakers. 

This election campaign was driven more by personality clashes than differences in policy.

Read the full BBC story about where Hillary Clinton and Donald Trump stand on the key issues. 

Image source, AFP

An election mapping platform built by Kenyan developers is being used to track possible voter intimidation and violence in the US election.

A team in Kenya and the US are working on the project, Ushahidi's innovation manager told the BBC.

Mr Trump has said he believes the election will be rigged and some fear his call for his supporters to monitor the voting process could lead to intimidation.

Mrs Clinton has dismissed voter fraud concerns.  

British politician Nigel Farage, a key figure in the campaign to take the UK out of the European Union at the referendum in June, has tweeted to say he hopes Tuesday will become America's own "Brexit day".

The UKIP leader has backed Donald Trump, appearing on stage with him in Jackson, Mississippi, in August.     

Donald Trump supporter Bruce Carter has had to battle hostility from fellow black voters on the streets of Philadelphia.  

The World at One
BBC Radio 4

Jonathan Josephs
BBC Business & Economics

Speaking on BBC World News, Mexican Tourism Minister Enrique De La Madrid Cordero said: "I really do not think that there is a contingency plan... Really what we are waiting for are the results of the election, but we are also concerned in the sense that all these speeches against trade which are not only happening in the US but worldwide, I think they are far away from the facts, trade is something that is positive for nations, today the world is integrating more when they produce." 

The minister added: "The way is to continue to produce together, to construct cars, computers, among our nations and we are very positive that is something that is going to continue to happen between the United States and Mexico in the years to come."

Mrs Clinton and Mr Trump disagreed about Nafta during a TV debate back in September.

Jonathan Josephs
BBC Business & Economics

Mexico's tourism minister has denied reports that his country has a contingency plan in case Donald Trump wins the US presidential election. Speaking to the BBC, he did express his government's concerns about any changes to free trade that might result from the election.

Both Hillary Clinton and Donald Trump have expressed concern about the North American Free Trade Agreement (Nafta), and Mr Trump has proposed a 35% tariff on imports of Mexican goods.

The World at One
BBC Radio 4

The World at One
BBC Radio 4

Emerging from the polling station near her home in Chappaqua, New York state, a smiling Mrs Clinton shook hands with supporters. "I'm so happy," she said. "I'm just incredibly happy. All my friends and my neighbours, it makes me so happy." She was escorted by her husband, former President Bill Clinton.

Image source, Reuters