We are closing our live coverage of the historic talks between US President Donald Trump and North Korean leader Kim Jong-un.

Both leaders have signed an agreement following the summit in Singapore. Here's what we know:

• North Korea has committed "to work towards the complete denuclearisation of the Korean peninsula" but analysts say it has not made specific commitments
• In a move that stunned observers, Mr Trump said the US would stop "provocative" war games with South Korea that have long infuriated the North
• Mr Trump also said North Korea had agreed to destroy a "major missile engine testing site"
• The US said sanctions on Pyongyang will not be lifted until progress is made on denuclearisation

You can read our full story here.

Image source, Reuters

China's foreign ministry announced the US would be suspending military exercises with South Korea before President Trump's press briefing, the BBC's Paul Danahar says.

It may show that Kim Jong-un's team informed Beijing as soon as the meeting was over.

It seems the historic summit has boosted President Trump's chances of winning the Nobel Peace Prize - at least in the eyes of the bookmakers.

They have slashed the odds on him winning following the summit.

Ladbrokes cut the odds from 10/1 to 6/4, and William Hill offered the same odds for Mr Trump and Kim Jong-un to win it jointly in the next couple of years.

But Mr Trump wouldn't be the first US president to bag the award.

In 2009, only a year into his term of office, US President Barack Obama won for "his extraordinary efforts to strengthen international diplomacy and co-operation between peoples".

Image source, AFP

The US ambassador to Nato, Kay Bailey Hutchison, has told BBC Newsnight that "there has to be verification" on denuclearisation, following the joint agreement.

But she praised the two leaders' first meeting, calling it "very strong".

President Trump's translator, longtime state department employee Lee Yun-hyang, was at times the only woman in the room during the negotiations between the US and North Korea.

According to reports in Korean media, she has worked for the US full time since 2009 and has translated for George W Bush, Barack Obama and Hillary Clinton.

She also was at Mr Trump's side when he met with the South Korean president , externalin May and when he greeted the US citizens who were released from North Korea last month, Quartz reports.

The 61-year-old's counterpart, North Korean Kim Ju-song, had previously met Mr Trump when he accompanied general Kim Yong-chol on his visit to the US in preparation for the summit.

The handshake between President Trump and Kim Jong-un was viewed by millions and represented the summit's major set piece.

We've looked back on some of history's most significant handshakes and why they mattered.

The Air China aircraft that Kim Jong-un arrived in has departed Singapore, according to a flight tracking website.

A second plane, likely carrying North Korean officials, has also left.

The path that led to this historic summit has been complicated and unpredictable, as has the relationship between President Trump and Kim Jong-un.

We've distilled the complex saga into 300 words.

Image source, Reuters

Senator Mark Warner, a Democrat who serves on the Senate Select Committee on Intelligence, argues that "Kim Jong-un walked away from Singapore with exactly what he wanted – the pomp, circumstance and prestige of a meeting with the President of the United States – while making no specific commitments in return".

Delaware senator Chris Coons added: "This was a dream outcome for Kim Jong-un... legitimacy on the world stage, an invitation to the White House, no concessions on human rights, and no clear concessions on a timeline or a process for denuclearisation."

"For this agreement with North Korea to mean anything, for it to be anything more than a reality TV handshake summit, there’s going to need to be a lot of hard work in the months ahead and I’m concerned that the Trump Administration isn’t prepared to do that hard work," Mr Coons said in an interview with MSNBC.

Image source, Getty Images

The British Foreign Secretary, Boris Johnson, just released a statement praising the "constructive summit", which he said is a "signal that Kim Jong-Un may have finally heeded the message that only a change of course can bring a secure and prosperous future to the people of North Korea".

"This is an important step towards the stability of a region vital to global economic growth and home to thousands of British Nationals and important UK interests," he says.

"There is much work still to be done and we hope Kim continues to negotiate in good faith towards complete, verifiable and irreversible denuclearisation.

"The UK will continue to support the United States in its efforts to achieve denuclearisation of the Korean Peninsula."

Nato - the North Atlantic Treaty Organisation - has praised the summit.

"Nato strongly supports all efforts leading towards the eventual denuclearisation of the Korean Peninsula," the head of the alliance said in a statement.

President Trump has been critical of Nato in the past. Last year, he branded it "obsolete" because it "wasn't taking care of terror".

President Trump's re-election campaign have issued a statement praising the summit.

"[Mr Trump] will continue to succeed in dramatic ways," it says. "He will always put America first and wishes only to succeed on behalf of the American people."

Image source, Getty Images

It's still only 08:00 local time in California, and Americans are still waking to learn of the historic meeting in Singapore.

In LA's Koreatown neighbourhood, a colourful mural depicting a possible visit of Kim to the US has gone up.

At the Santa Monica pier, a pair of impersonators have been attracting loads of attention in recent days, as anticipation of the talks built up.

Image source, Getty Images

Image source, Getty Images

Image source, Getty Images

Image source, Getty Images

Image source, Getty Images

The Republican Chairman for the House Foreign Affairs Committee, Ed Royce, just sent us this statement.

"Protecting America from North Korea’s nuclear threats is an urgent priority, and I’m glad the president is seeking peace through diplomacy. Kim Jong-Un has gained much from step one, including an apparent promise from the president regarding important US-South Korea defensive military drills."

The California congressman adds that he is looking forward to a "detailed briefing" on the talks, and that "congress has an important oversight role in this process".

"Kim Jong-Un should not receive a dime of relief until he fully and verifiably denuclearises," he concludes.

Image source, Pool

"Resolving this 65-year old international challenge will take a great deal of hard work," Republican majority leader Mitch McConnell said minutes ago on the floor of the US Senate.

He says that he supports the goals, as outlined in the joint statement, but adds that "if North Korea does not prove willing to follow through, we and our allies must be prepared to restore the policy of maximum pressure."

"Today, I congratulate the president on this major step, and share his hope that it will begin a process that leads to an historic peace."

Trump tells Voice of America, the US government-sponsored news network, that Kim "liked" him.

"I think he liked me and I like him. And I understand the past and, you know, nobody has to tell me - he’s a rough guy. He has to be a rough guy or he has been a rough person."

The interviewer, Greta Van Susteren, says: "But he's starved them. He's been brutal to them. He still loves his people?"

"Look, he’s doing what he’s seen done, if you look at it," says Trump.

"But, I really have to go by today and by yesterday and by a couple of weeks ago because that’s really when this whole thing started."

Asked what his message is for the North Korean people directly, Trump says:

"Well, I think you have somebody that has a great feeling for them.

"He wants to do right by them and we got along really well. We had a great chemistry - you understand how I feel about chemistry. It’s very important."

"I mean, I know people where there is no chemistry, no matter what you do you just don’t have it. We had it right from the beginning, I talked about that and I think great things are going to happen for North Korea."

North Koreans switching on the news are not seeing any reports on the historic meeting between leader Kim Jong-un and President Trump.

State broadcaster Korea Central Television mentions the Supreme Leader's trip to Singapore but nothing of the summit.

Here's what they saw

Did Donald Trump and Kim Jong-un strike a win-win deal at their summit, or was it just a Kim win?

There is further reaction from Republican Senator Marco Rubio, who takes issue with President Trump's description of Kim Jong-un as "talented".

"Well, he is very talented," Mr Trump said. "Anybody that takes over a situation like he did at 26 years of age and is able to run it and run it tough. I don't say he was nice."

Mr Rubio shared a somewhat less favourable view of the North Korean leader's credentials.

The North Korean leader has left his hotel, Yonhap reports.