US President Donald Trump and North Korean leader Kim Jong-un sign an agreement in Singapore
North Korea "commits to work towards the complete denuclearisation of the Korean peninsula" but analysts say it has not made specific commitments
Mr Trump later defends what he has achieved and stuns observers by saying the US will stop war games with South Korea that infuriate the North
He says Mr Kim agreed to destroy a "major missile engine testing site" and that sanctions won't be lifted until progress is made on denuclearisation
The summit is the first time a sitting US president has ever met a North Korean leader
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
Mr Kim's motorcade has also now left the island of Sentosa. He's expected to be heading out of Singapore very soon.
Image source, ReutersMr 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.
Image source, ReutersBeijing 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.
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.
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.
Here's what just happened;
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."
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.
Sadly, we can't zoom in and see.
Kelly O'Donnell, White House correspondent at NBC News, tweets:
The leaders have signed, smiled, shaken hands, and moved on.
We wait now to find out what they signed. Mr Trump said copies would be handed out to reporters shortly.
"Thank you very much, that was fantastic," Mr Trump tells Mr Kim as they smile and shake hands.
Mr Trump tells reporters: "We're very proud of what happened today. Our whole relationship with North Korea and the Korean peninsula will be a much different situation than it has in the past."
Mr Kim says through a translator, "we've decided to leave the past behind".
"The world will see a major change," he says.
We don't yet know what it says, only that it's "historic" and "comprehensive".
Mr Kim and Mr Trump enter the room to deafening camera clicks.
Mr Trump says they're signing a "pretty comprehensive document".
If you're time pressed and want a quick summary of the North Korea situation, here's our 300-word explainer.