US Secretary of State Mike Pompeo has tweeted an action photo of himself telling Japanese and South Korean foreign ministers Taro Kano and Kang Kyung-wha what Mr Trump and Mr Kim said to each other.

Our Asia business correspondent Karishma Vaswani debunks some of the myths.

There were a few Korean dishes but if Trump chose carefully he could have been in 1980s New York.

Journalist Martyn Williams has spotted that at the last minute before the signing, Kim Jong-un's sister Kim Yo-jong swapped the pens so Kim would not sign the document with a Donald Trump pen.

You can read more about Kim Yo-jong on the BBC website.

China's official Xinhua news agency has posted a commentary on the Trump-Kim summit.

It said the meeting had "ignited hopes for a political solution to the Korean peninsula nuclear issue", but adds:

"No one, however, would expect the half-day summit to be able to iron out all differences and remove deep-seated mistrust between the two long-time foes.

"The road toward the goal of a nuclear-free peninsula and realizing regional peace and prosperity is bound to be a bumpy one that requires patience and wisdom. The first step is always the hardest to take."

The full commentary can be read here, external.

BBC Monitoring
The world through its media

North Korean state television has started at its usual time of 0600 gmt on 12 June, but it has made no mention yet of leader Kim Jong-un’s meeting with US President Donald Trump in Singapore a short while earlier.

Korean Central Television (KCTV) began broadcasting at 0600 gmt - which is 1500 hours local time - and carried news of Kim’s Singapore tour the previous day even as international media outlets have been showing live coverage of the summit between him and Trump.

After starting with patriotic music and the day's broadcast schedule, around 0610 gmt the TV channel instead carried a short clip featuring a female news anchor talking about Kim's visits to popular sights in Singapore, without photos or footage of his tour.

Jenny Town, Korea analyst and editor at 38North, external, has been analysing Kim Jong-un’s reception in Singapore - replete with a myriad of political handshakes and selfies - for the BBC.

The summit is a "huge win for Kim-Jong-un… the optics literally couldn’t have been better if he had tried to stage it himself”, she says.

“The fact is this is Kim Jong-un - six months ago he was one of the world’s most hated leaders, and now he’s [being treated like] a political rockstar.”

Image source, Reuters

This is a summit where nothing goes unscrutinised - and so Northeast Asia analyst John Nilsson-Wright has been looking for clues in the two leaders' signatures.

Trump's gives off "short term get-the-job-done self assurance", he says.

Kim's meanwhile screams "soaring, aspirational all-to-play-for ambition".

Analysts and correspondents have been poring over the leaders' declaration and some have given their reaction on Twitter.

It's fair to say these observers are not that excited by what they've read.

In Beijing, Foreign Minister Wang Yi described the Singapore summit as an "equal dialogue" between Donald Trump and Kim Jong-un. He also said it was exactly what China had always wanted. He also added that "no one will doubt the unique and important role played by China: a role which will continue."

Experts say China will be keen on any de-escalation in tension between the two sides - but will also be wary of being excluded from negotiations.

Trump gives his reaction after he and Kim sign a document the US president described as "comprehensive".

"We're very proud of what took place today," he said.

"We both want to do something, we both are going to do something," he added.

The BBC's Laura Bicker has the four key points from the Trump-Kim Declaration:

1. The United States and the DPRK [Democratic People's Republic of Korea] commit to establish new US-DPRK relations in accordance with the desire of the peoples of the two countries for peace and prosperity.
2. The United States and the DPRK will join their efforts to build a lasting and stable peace regime on the Korean Peninsula.
3. Reaffirming the April 27, 2018 Panmunjom Declaration, the DPRK commits to work towards the complete denuclearisation of the Korean peninsula.
4. The United States and the DPRK commit to recovering POW/MIA remains including the immediate repatriation of those already identified.

Details are coming through on the agreement. According to the AFP news agency, Mr Kim has committed to the "complete denuclearisation" of the Korean peninsula.

That sound big - but he has committed to that already, in talks with South Korea, and we still don't know what it entails.

BBC Monitoring has the front page of North Korea's Rodong Sinmun newspaper - which carries a series of photos of Mr Kim's walkabout in Singapore before his meeting with Mr Trump.

Meanwhile North Korean TV is broadcasting its regular opening sequence.

Kim Jong-un did not travel abroad during the first six years of his tenure, which many pundits attributed to his fear of a coup in his absence. But, in 2018, he has already visited China twice, crossed over to South Korea, toured Singapore, and might even visit Russia in September, say BBC Monitoring.

While much of the world's attention is focused on the summit, much less is known about who is running the reclusive country while the Supreme Leader is away, say our colleagues at BBC Monitoring.

Mr Kim arrived in Singapore on 10 June, accompanied by his influential sister Kim Yo-jong and his right hand man Kim Yong-chol.

But, crucially, he left 90-year-old ceremonial head of state Kim Yong-nam and Choe Ryong-hae, another senior leader, in Pyongyang, apparently in charge.

The BBC's Rupert Wingfield-Hayes says the summit amounts to a huge victory for the North Korean leader.

"It's a very big win for Trump to be saying the whole relationship is different from the past and he's honoured to be with him.

"These are extraordinary things to be saying about a man who just a few months ago was being described as 'little rocket man' and considered as the leader of a regime that was reviled around the world," our correspondent says.

It looks like Mr Trump is actually still on Sentosa - he is expected to speak to the press there later on, at the Capella hotel where the mysterious document was signed.

The BBC's Mariko Oi is live on Facebook now., external She's along the route Mr Kim will be taking back to his hotel.