Both sides are playing down expectations of a major breakthrough, but some analysts believe genuine progress could be made.

Having borrowed a Chinese jet to fly into Singapore amid fears North Korea’s own planes might not make the journey, the nation’s so-called supreme leader this time embarked on a two-day train journey to get to Hanoi. Mr Trump took off on Air Force One on Monday.

While their first meeting was unquestionably historic – no sitting US president had met before with a North Korean leader – some questioned how much Mr Trump secured in exchange for providing legitimacy to a nation that had broken international treaties to develop a nuclear weapon.

So, just what can be expect from the second meeting of the two leaders?

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What did they achieve in Singapore?

Plenty of people said the first meeting delivered little and the vague commitment to the complete denuclearisation of the Korean peninsula contained few details. Critics said Mr Trump, in his typical style, oversold the deal brokered during five hours of talks. “I do trust him, yeah,” he told ABC News, in an interview from the city state. “Now will I come back to you in a year, and you’ll be interviewing, I’ll say, ‘Gee I made a mistake’? That’s always possible.”

But perhaps the most important achievement was the change in the narrative. Just months before the meeting, Mr Trump and Mr Kim had been exchanging threats about “fire and fury” and the size of their nuclear arsenals. Such was the anxiety that in January 2018, people in Hawaii ran for cover after a false ballistic missile alert was sounded. People were genuinely scared that conflict could break out.

“The main achievement was changing that narrative of one of potential conflict to one of two countries that had the potential to do a deal,” said Yun Sun, a regional expert and co-director of the East Asia programme at the Stimson Centre, a DC-based think tank that works on peace issues.

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What has (and has not) happened since Singapore?

One criticism of the big headlines Mr Trump and Mr Kim made last summer was that they were then not followed up by solid achievements by envoys. Western analysts say that because Mr Kim’s power is all-embracing, it is harder for his diplomats to make agreements.

A similar point could be made about Mr Trump. Secretary of state Mike Pompeo and national security adviser John Bolton both interact with North Koreans at a high level, but Pyongyang knows Mr Trump could change his mind in an instant and any agreement rendered meaningless.

Following the meeting, Reuters said North Korea repatriated 55 boxes containing what were believed to be the remains of American soldiers; in July, satellite images indicated North Korea had begun to dismantle some facilities at its Sohae satellite launching station; North and South Korea moved forward with their own reconciliation.

But US intelligence officials have said North Korea has continued to develop its nuclear and missile arsenals, despite a self-imposed moratorium on testing.

What would each side like from Hanoi?

Put simply, North Korea would like to see some sort of sanctions relief – whether from US sanctions, international sanctions or those enforced by South Korea. The US would like to see something tangible to convince it that North Korea is serious about denuclearisation.

“Progress for Pyongyang is and has always meant regime survival,” said Paul Carroll, a North Korea expert and a senior adviser at N Square, based in San Francisco.

“Any sanctions relief would be a gain, any statements that downgrade the status of the decades long armistice would be a gain, and rhetoric from Trump that conveys less threat from Kim and more legitimacy would be a gain. In concrete terms, sanctions relief, food aid, would be tangible ‘progress’.”

He said from the US perspective it would like specific, time-bound commitments from North Korea on its behaviour with respect to its nuclear programme and its willingness to allow verification.

“For example, it has said it would allow inspections of some sort at the Yongbyon facilities. Great, but what exactly and for how long and by whom?” he said. “Continued moratoria on nuclear and long-range missile tests would also be progress – it would essentially cap any improvements of their programme.”

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What would represent genuine progress?

Analysts warn not to expect too much, and that the reshaping of the relationship between the US and North Korea will take decades. But there is room for optimism about modest progress. Indeed, Daryl Kimball, executive director of the Arms Control Association, said he was more hopeful about this summit than the first.

One possible outcome, he said, would be a formal end of the Korean War, which the North has long called for as a major step towards normalising ties. “That would be symbolic,” he said. “It would show Trump is serious about the US taking steps to change the relationship.”

After meeting with Mr Kim in September, South Korean president Moon Jae-in said the North was willing to “permanently dismantle” its Yongbyon nuclear complex and allow international inspectors into some missile sites if the United States makes concessions of its own.

In exchange, the United States could also agree to opening US-North Korea liaison offices and allow some inter-Korean projects, provided the North takes steps towards denuclearisation, Reuters said.

Mr Sun said a win-win for both sides would involve agreeing to a road map that identified further steps. “If North Korea allows IAEA [International Atomic Energy Agency] inspections, that would be a meaningful step.”

Mr Trump has suggested he is in no rush. He said: “I just don’t want testing. As long as there’s no testing, we’re happy.”