Donald Trump and Kim Jong-un have become the first sitting US president and North Korean leader to meet, an unprecedented development after a year of exchanging threats.
The pair shook hands at a luxury hotel on Singapore’s Sentosa island before proceeding to talks.
After the summit the leaders signed a “comprehensive” document, promising a new relationship between the nations.
They had been discussing defusing tensions and nuclear disarmament.
The document commits North Korea to work towards “the complete denuclearisation of the Korean peninsula” and promises “new relations” between Washington and Pyongyang.
The US had demanded “complete, verifiable and irreversible denuclearisation”.
There was also a commitment to build “a stable and lasting peace” on the Korean peninsula.
“I think both sides will be very impressed with the result,” Mr Trump said at a signing ceremony with Mr Kim.
Mr Trump spoke of a “special bond” with the North Korean leader and said he was “absolutely” willing to invite him to the White House.
“We’ve decided to leave the past behind,” Mr Kim said. “The world will see major changes.”
Still, analysts remain divided on what the summit will ultimately achieve. Some see it as a propaganda win for Mr Kim, others a potential path to peace.
How the historic moment unfolded
The summit began with a striking image, unimaginable just months ago.
The two men walked towards each other and firmly gripped each other’s hands in front of US and North Korean flags.
Mr Trump patted Mr Kim’s arm as they stood on red carpet and exchanged a few words before turning to face the gathered press.
“I feel really great. We’re going to have a great discussion and will be tremendously successful,” the US president said.
Sitting alongside each other, ahead of a one-on-one meeting, the pair appeared relaxed against the odds.
“It was not easy to get here,” Mr Kim said. “There were obstacles but we overcame them to be here,” and his counterpart responded “That’s true.”
Singapore’s taxi drivers on the summit
The two men, accompanied only by interpreters, spoke for a little under 40 minutes. They were then joined by small delegations of advisors for a working lunch.
From Washington the group included US Secretary of State Mike Pompeo and security adviser John Bolton, and on Pyongyang’s side, Mr Kim’s “right-hand man” and former spy chief Kim Yong-chol, and foreign minister Ri Yong-ho.
Over lunch they shared a mix of Western and Korean dishes, including stuffed cucumbers and Daegu jorim, a soy-braised fish dish.
What does this mean for each man?
The unprecedented event carries great potential prestige for each leader – but also, in the long run, a possibly catastrophic loss of face.
For the moment Mr Trump will credit any successful outcome of talks to his “maximum pressure” campaign on North Korea, that tightened economic sanctions and threatened military action. Many believe that no matter what is achieved this will be the narrative.
For Mr Kim, securing a stage with the US leader is seen as a victory in itself, something which neither his father or grandfather could achieve.
Such a meeting has long been seen as a prize in the eyes of North Korea for the legitimacy it would confer on its leader.
For decades, North Korea has been a pariah state, and now its latest hereditary leader is being treated as a world statesman.
Last year, it would have been a rare sight to see a North Korean flag flying anywhere in Asia.
Now, Mr Kim – who runs a totalitarian regime with extreme censorship and forced-labour camps – is meeting and greeting dignitaries.
On the eve of the summit, Mr Kim toured Singapore’s tourist sites, waving to excited crowds and snapped a selfie with the city state’s foreign minister.
Tuesday’s front page of North Korea’s official newspaper featured the extraordinary scenes on display in Singapore, offering many in the country an unprecedented glimpse of their leader in a setting utterly at odds with their daily life.
How did we get here?
This is an outcome that seemed unimaginable less than a year ago – when Mr Trump and Mr Kim exchanged streams of fiery insults – and North Korea conducted several ballistic missile tests in defiance of the international community.
How well has Trump prepared for Singapore?
Mr Trump famously vowed to unleash “fire and fury” if Pyongyang kept threatening the US. Meanwhile, Mr Kim has called Mr Trump “mentally deranged” and a “dotard”.
But earlier this year North Korea showed a new openness to diplomacy and held direct talks with Seoul. The rapid improvement in relations between the North and South Korea – technically still at war – culminated with a historic leaders’ summit in April.
During this warming of relations between the two Koreas, Mr Trump stunned the world by accepting an invitation to meet Mr Kim.