On Tuesday, Trump and Kim signed a statement outlining four points, including reaffirming a commitment to denuclearize the Korean peninsula.
And now here we are, talking seriously about not-nuking each other.
Moon issued a statement after the summit calling it a "huge step forward" toward peace that "helped break down the last remaining Cold War legacy on Earth".
The move, long requested by Pyongyang, has been seen as a major concession to North Korea and has left one former South Korean military leader "speechless". "We're going to have a great discussion and will be tremendously successful". "He's clearly executing people", Baier said.
He lavishly praised the young dictator, saying he trusted him to "do the right thing"; this despite decades of evidence that the Kim family had cemented its dynasty with ruthlessness and duped the global community about its nuclear weapons programme.
After a day filled with smiles and handshakes watched around the world, the U.S. "committed to provide security guarantees" to North Korea.
"India welcomes the United States-DPRK (Democratic People's Republic of Korea) Summit held in Singapore".
The move - long demanded by Pyongyang - has been seen as a major concession to North Korea and appeared to take United States allies in the region by surprise.
In return, Trump has promised to stop US military drills in South Korea.
The news agency said that Kim invited Trump to visit Pyongyang "at a convenient time" and that Trump also invited Kim to visit the US.
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"Why did South Korea and the USA form an alliance and stage military drills before the nuclear crisis flared?"
Most of all, I think they feel relief - relief they would not have felt, and certainly not to the same degree, if the Democrats hadn't drummed up hysteria about an impending war with North Korea. Trump said: "That's true".
"I think he's going to do these things", Trump said. A major challenge, according to these officials, is to turn Trump's broad intentions into detailed military guidance.
WATCH: Was the North Korea summit a success or a fail? But he kept trying to reach out to North Korea, and eventually found a role as a mediator after Kim offered in January to send a delegation to the South Korean Winter Olympics.
Pyongyang in return "commits to work toward complete denuclearisation of the Korean peninsula".
Trump has defended the agreement as a major step in dealing with the threat of nuclear-armed North Korea and said he believed Kim's government would start the process of living up to the agreement right away.
Trump first announced there would be "a signing" shortly after midday, during a stroll with Kim around the hotel grounds.
However, some are still wary of the nature of the summit, with some saying the document signed between the two leaders looks "scarily like a draft agreement".
Both leaders signed a document pledging to work toward "complete denuclearization of the Korean Peninsula" on Tuesday.
At a news conference in Seoul, Secretary of State Mike Pompeo was asked if the Pentagon and the South Koreans had been asked for their views.
Bong Youngshik, a professor at Seoul's Yonsei University, said it's too early to predict how Trump's cancellation of the military drills will play out in future nuclear negotiations. He said North Korea is likely to consider Trump's decision a temporary measure while it remains in negotiations with Washington. Trump will likely benefit politically from that sense of relief.