The BBC's Laura Bicker has the four key points from the Trump-Kim Declaration:
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.
The United States and the DPRK will join their efforts to build a lasting and stable peace regime on the Korean Peninsula.
Reaffirming the April 27, 2018 Panmunjom Declaration, the DPRK commits to work towards the complete denuclearisation of the Korean peninsula.
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.
How N Korea's media is covering the day
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.
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.
Who's in-charge while Kim is away?
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.
'A big win for Kim'
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.
Trump to speak to press on Sentosa
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.
In response to a question about whether they had reached an agreement on denuclearisation - the nebulous term which has underpinned their entire interaction - Mr Trump says they will be "starting this process very quickly".
Here's a short explainer of why it's such a tricky term.
Denuclearisation: The word Trump and Kim can't agree on
And Kim's off too
Mr Kim's motorcade has also now left the island of Sentosa. He's expected to be heading out of Singapore very soon.
Reuters
And they're leaving the island
Mr Trump's convoy has left Sentosa - the island where the meeting took place. He's crossing the short cause way to the Singapore mainland. He's said he'll talk to the press later. Mr Kim, meanwhile, is expected to leave Singapore within hours.
Reuters
Praise from China
Beijing has applauded the summit between
US President Donald Trump and North Korean leader Kim Jong-un, calling it historic.
The fact that the two leaders "can sit together and have equal talks has
important and positive meaning, and is creating a new history," Foreign
Minister Wang Yi said.
He also reiterated Beijing's call for "full denuclearisation" to resolve tensions on the Korean peninsula.
"Absolutely, I will." -- @realDonaldTrump on whether he would invite Kim Jong Un to the White House. #KimTrump
'Comprehensive is a big word'
Prof Robert Kelly tells the BBC that there is speculation in the South Korean media that the mystery document signed by both leaders is a peace treaty - but if this were the case it would also have to involve South Korea, he says.
The fact that Donald Trump said it was "comprehensive" suggests it could cover other issues such as human rights, sanctions and economic aid.
"Comprehensive is a big word," Prof Kelly says on the BBC.
Did they address human rights?
Probably not. Asked whether they spoke about Otto Warmbier, they didn't respond.
BTW, the question to Kim and Trump "Did you talk about Otto Warmbier?" was ignored by both Kim and Trump.
Recap on that briefing
Here's what just happened;
US President Donald Trump and North Korean leader Kim Jong-un signed a document - we don't know what it said.
Mr Trump said it was "very important" and "pretty comprehensive" and that he and "Chairman Kim" were "both very honoured" to sign it.
Mr Kim said they had a "historic meeting and decided to leave the past behind".
He thanked Mr Trump "for making this meeting happen".
'He loves his country'
Donald Trump says it's been a "terrific day".
"We've learned a lot about each other and about our countries."
About Kim Jong-un he said: "He's a very talented man and he loves his country very much."
A 'special bond'
Donald Trump, the president of the US, says he has developed a "special bond" with Kim Jong-un, until today one of the most shunned leaders of one of the most isolated countries on Earth.
Live Reporting
By Anna Jones, Andreas Illmer, Heather Chen, Yvette Tan and Minji Lee
All times stated are UK
Get involved
'We both want to do something'
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.
BreakingA four-point declaration
The BBC's Laura Bicker has the four key points from the Trump-Kim Declaration:
Kim 'commits to complete denuclearisation'
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.
How N Korea's media is covering the day
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's travels in 2018
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.
Who's in-charge while Kim is away?
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.
'A big win for Kim'
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.
Trump to speak to press on Sentosa
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.
Facebook live from central Singapore
The BBC's Mariko Oi is live on Facebook now. She's along the route Mr Kim will be taking back to his hotel.
Denuclearisation?
In response to a question about whether they had reached an agreement on denuclearisation - the nebulous term which has underpinned their entire interaction - Mr Trump says they will be "starting this process very quickly".
Here's a short explainer of why it's such a tricky term.
And Kim's off too
Mr Kim's motorcade has also now left the island of Sentosa. He's expected to be heading out of Singapore very soon.
And they're leaving the island
Mr Trump's convoy has left Sentosa - the island where the meeting took place. He's crossing the short cause way to the Singapore mainland. He's said he'll talk to the press later. Mr Kim, meanwhile, is expected to leave Singapore within hours.
Praise from China
Beijing has applauded the summit between US President Donald Trump and North Korean leader Kim Jong-un, calling it historic.
The fact that the two leaders "can sit together and have equal talks has important and positive meaning, and is creating a new history," Foreign Minister Wang Yi said.
He also reiterated Beijing's call for "full denuclearisation" to resolve tensions on the Korean peninsula.
A White House invitation
'Comprehensive is a big word'
Prof Robert Kelly tells the BBC that there is speculation in the South Korean media that the mystery document signed by both leaders is a peace treaty - but if this were the case it would also have to involve South Korea, he says.
The fact that Donald Trump said it was "comprehensive" suggests it could cover other issues such as human rights, sanctions and economic aid.
"Comprehensive is a big word," Prof Kelly says on the BBC.
Did they address human rights?
Probably not. Asked whether they spoke about Otto Warmbier, they didn't respond.
US student Otto Warmbier was arrested in North Korea in 2016, held there for months and died shortly after he was eventually brought back to the US in 2017 in a coma.
Recap on that briefing
Here's what just happened;
'He loves his country'
Donald Trump says it's been a "terrific day".
"We've learned a lot about each other and about our countries."
About Kim Jong-un he said: "He's a very talented man and he loves his country very much."
A 'special bond'
Donald Trump, the president of the US, says he has developed a "special bond" with Kim Jong-un, until today one of the most shunned leaders of one of the most isolated countries on Earth.
But what does it actually say?
Sadly, we can't zoom in and see.