The moment they shook hands US President Donald Trump says his historic talks with North Korean leader Kim Jong-un that ended in a joint agreement were "tremendous".
The signed document includes a pledge from Mr Kim to rid the Korean peninsula of nuclear weapons.
But in an extraordinary media conference later, Mr Trump announced details not in the paper.
He said he would halt US military exercises in South Korea, something widely seen as a concession.
Last year saw the pair sling insults at each other, while North Korea conducted several ballistic missile tests in defiance of the international community. For both men the meeting brought much to gain as well as considerable risk.
The meeting is seen by North Korea as a way of bringing legitimacy to a nation long regarded as a pariah. Should Mr Trump resolve the North's nuclear threat, he would have achieved something none of his predecessors came close to.
The agreement said the two countries would co-operate towards "new relations", while the US would provide "security guarantees" to North Korea.
On nuclear weapons, Mr Kim "reaffirmed his firm and unwavering commitment to complete denuclearisation of the Korean peninsula".
Observers say the document lacks substance, in particular on how denuclearisation would be achieved.
However, speaking to reporters after, Mr Trump said:
The US would suspend "provocative" war games it holds with South Korea. Mr Trump said he wanted to see US troops withdraw from the South.
A spokesperson for the US forces said they had yet to receive any new guidance On denuclearisation, he said that Mr Kim had agreed to it being "verified", a key US demand ahead of the meeting.
Mr Trump said Mr Kim had also agreed to destroy a "major missile engine testing site" But he said sanctions would remain in place for now and argued "we haven't given up anything".
Several reporters asked whether Mr Trump had raised the issue of human rights with Mr Kim, who runs a totalitarian regime with extreme censorship and forced-labour camps.
Trump said : "The past does not have to define our future"
"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."
In a post-summit interview with ABC News, the president said he was confident that the agreement meant full denuclearisation.
"Yeah, he's de-nuking, I mean he's de-nuking the whole place. It's going to start very quickly. I think he's going to start now," he said."I think he trusts me and I trust him," Mr Trump added.
Largely positive. South Korean President Moon Jae-in, who held his own meeting with Mr Kim earlier this year, said the "two Koreas and US will write new history of peace and co-operation".
China, North Korea's only major diplomatic and economic ally, also said the meeting created a "new history". The foreign ministry said sanctions on North Korea could be eased if it stuck to UN resolutions.
Japanese Prime Minister Shinzo Abe praised President Trump's "leadership and effort", saying he supported North Korea's pledge on denuclearisation as "a step towards the comprehensive resolution of issues around North Korea".
But Russia warned that the "devil is in the detail" and Iran said North Korea should not trust the US. Mr Trump recently pulled the US out of a nuclear deal with Iran.
It is true the Singapore summit was certainly historic, but the results are harder to judge.