The two men clasped hands beneath the white-washed walls of an upscale hotel in neutral Singapore, before sitting down for a half-day of meetings with major ramifications for the region and the world.

It is the first-ever meeting between sitting leaders of the two nuclear-armed foes and was unthinkable just months ago, when fears of war mounted amid missile tests and verbal insults.

The pair shook hands for several seconds, Trump reaching out to touch the North Korean leader on his right shoulder.

As they sat down for their tete-a-tete, the US leader -- who had said he would know "within the first minute" if a deal would be possible -- predicted a "terrific relationship" with Kim.

For his part, the North's leader made a reference to the two countries' history of war and acrimony, but noted the fact of their meeting showed they could overcome the past.

Sitting across from Trump at a small side table, Kim told the US president through a translator: "It was not easy to get here."

"The past worked as fetters on our limbs and the old prejudices and practices worked as obstacles on our way forward," he went on, his listener looking him in the eye and nodding. "But we overcame all of them and we are here today."

Trump responded: "That's true" before another handshake -- smiling this time -- and a thumbs-up from the US president.

The imagery for the high-stakes meeting was undoubtedly positive and Kim Yong-hyun, professor at Dongguk University in Seoul said: "The atmosphere of the summit looks very good."

"It will be hard for this meeting to agree on specific deals but it carries considerable significance as a starting point," he said.

After huddling for around 40 minutes, the leaders were joined by senior advisors before breaking for lunch, with prawn cocktail, short-rib confit, soy-braised cod, and vanilla ice-cream among the options.

- 'Fire and fury' -

Some analysts have warned the summit could produce more style than substance and Kelly Magsamen, a former top Pentagon Asia specialist, said: "We'll see if Kim actually gives him anything more than superficial pleasantries and some good TV."

But the warm words and positive optics seemed a different era from when Trump was threatening to rain down "fire and fury" on Pyongyang and Kim attacked Trump as a "mentally deranged US dotard", as he fired off a series of provocative weapons tests.

Trump had cajoled the international community to exert "maximum pressure" to buckle Kim's regime if he did not give up his nuclear weapons.

The Singapore summit is a potentially legacy-defining meeting for both men -- comparable to president Richard Nixon's 1972 visit to China, or Ronald Reagan's 1986 summit with Mikhail Gorbachev in Reykjavik.

And it is part of what Trump calls a "one-time" offer to resolve the stand-off through diplomacy.

Many agreements have been made in the past with North Korea that have later fallen apart.

On the table is the vexed question of denuclearisation -- a word that means vastly different things to the two parties.

It remains far from clear that Pyongyang is willing to give up its nukes -- weapons that the regime sees as its ultimate guarantee of survival.

And on the eve of the meeting, aides for both men were still scrambling to narrow yawning differences.

Secretary of State Mike Pompeo said Monday that the United States was willing to offer Pyongyang "unique" security guarantees if it denuclearises.

- Hugely symbolic -

The pair -- Kim in his thirties and consolidating his dictatorship, Trump in his seventies and struggling to bend Washington to his impetuous will -- are unlikely protagonists, both instantly recognisable, so much larger than life as to be cartoonish.

But their work Tuesday was deadly serious.

They represent nations that are still technically at war, even if the mortars, carbines and gunships of the bloody 1950s conflict have long since fallen silent.

The totalitarian regime has made rapid progress towards marrying nuclear and missile technology that would put Los Angeles, New York and Washington within striking distance of a nuclear weapon.

The United States says that is unacceptable and will be dealt with, one way or another.

For North Korea the talks are hugely significant and the image of Kim and Trump standing before the flags of both countries is an enormous step towards ending decades of international isolation.

Trump will use what he says are legendary instincts to see whether Kim if bluffing, buying time or is serious.

But the summit itself is unlikely to be the end game -- more likely it is the start of a longer process of negotiation.

The discussions "will set the framework for the hard work that will follow", Pompeo said.

South Korean President Moon Jae-in echoed the feelings of many on the troubled peninsula and beyond.

"I, too, could hardly sleep last night," he told his ministers as they watched the handshake live before a cabinet meeting, voicing hopes for a "new era among the two Koreas and the United States".