This time, the heads of the two nuclear-armed nations are squaring off in Vietnam for two days of talks that are set to focus on many of the same issues they debated last June in Singapore.
Trump is pushing North Korea to give up its nuclear weapons as he dangles the prospect of an economic boost to the repressive isolated country. Kim wants to see sanctions eased without losing the strategic benefits of his weapons of mass destruction.
The summit kicked off with a brief one-on-one meeting between the two leaders at the historic Metropole hotel in Hanoi. Trump and Kim were then joined by Secretary of State Mike Pompeo, acting White House chief of staff Mick Mulvaney and two North Korean officials for what the White House deemed a "social dinner."
In a brief statement while seated next to Kim for a pre-dinner photo op, Trump said he hoped this week's summit will be "equal or greater" in terms of results than last year's meeting. He emphasized his personal connection to the autocratic leader, saying their relationship had made "the biggest progress."
"Your country has tremendous economic potential — unbelievable, unlimited — and I think that you will have a tremendous future with your country, a great leader," Trump said, looking directly at his North Korean counterpart. "I look forward to watching it happen and helping it to happen — and we will help it to happen."
Speaking to reporters from the dinner table, Trump said he and Kim have "a very special relationship."
Earlier in the day, Trump met with Vietnam's president and prime minister, and repeatedly suggested that North Korea could realize a "thriving" economy if only it plays ball with the U.S.
Most news from the U.S.-North Korea summit is likely to come on Thursday. The two sides are expected to hold meetings throughout the better part of that day, and some form of statement or signing is likely at the summit's conclusion.
That was how Trump and Kim closed their summit in Singapore last June. The leaders held a signing ceremony for a declaration that said both sides would commit to establishing better relations and that North Korea "commits to work toward complete denuclearization of the Korean Peninsula."
Last year's meeting marked the first in-person meeting between a sitting U.S. president and a North Korean head of state.
Trump heralded that agreement as "very comprehensive," but outside observers played down its importance because of a recurring diplomatic issue with Pyongyang: North Korea has a different definition for "denuclearization" than others.
Pyongyang has said in the past it may denuclearize only if certain conditions were fulfilled. Those include the U.S. withdrawing troops from South Korea as well as ending the U.S. regional nuclear umbrella, a security arrangement in which Washington promises in-kind retaliation on behalf of close allies if they are attacked with nuclear weapons.
American and North Korean sides still appear far apart on the idea of North Korea getting rid of its nuclear weapons.
"So far, North Korea seems only willing to take measures that limit its nuclear and missile capabilities — it has no indications that it wants to roll back or undercut its existing nuclear arsenal or missile arsenal," Tong Zhao, a fellow at the Carnegie-Tsinghua Center for Global Policy, told CNBC on Tuesday.
Reports since the last Trump-Kim summit suggest North Korean forces are continuing to develop missile technology and nuclear weapons in secret facilities. A U.S. intelligence report last month said North Korea was "unlikely to give up" its weapons of mass destruction, missiles or production capability.
Trump has repeatedly pointed out that no one has detected North Korea testing nuclear devices or ballistic missiles since his administration began engaging with the Kim regime in earnest.
For a period in 2017 — Trump's first year in office — North Korea created global anxiety by testing missiles at least once a month and directing regular threats toward the United States and others. Trump declared in August 2017 that such threats "will be met with fire and fury like the world has never seen."
Pyongyang is last known to have conducted a nuclear test in September 2017 and an intercontinental ballistic missile test in November 2017.
As Kim and Trump face off in Hanoi, analysts say neither is politically incentivized to aim for big concessions.
"For both leaders, a limited amount of progress is going to be success enough," said Richard Fenning, CEO of risk consultancy Control Risks. "This, I think, is a kind of continuity summit."
Fenning and others have forecast that Thursday's talks will likely conclude with an agreement that includes opening representative offices in each other's countries and potentially some move to officially declare an end to the Korean War (the fighting stopped in 1953 following an armistice).
Trump, for his part, has appeared to play down the goals for the summit. Whereas last year he claimed the North Korean regime would begin removing its nuclear capabilities "very, very quickly," he said last week that he was in no hurry.
"Well, I'd just like to see, ultimately, denuclearization of North Korea. I think we will see that ultimately. I have no pressing time schedule," he said from the Oval Office last week. "And I think a lot of people would like to see it go very quickly from the other side."
"But I'm in no rush. There's no testing," Trump added. "As long as there's not testing, I'm in no rush. If there's testing, that's another deal."
Still, after his meetings with the Vietnamese officials and before his dinner with Kim, Trump said in a Twitter post that he remained committed to pursuing denuclearization.
As for North Korea's goals, analysts said the country is probably willing to remove some capabilities it no longer needs and may agree not to increase the size of its arsenal. But Kim won't give up his nuclear weapons, they said.
Victor Cha, Korea chair at the Center for Strategic and International Studies, predicted during a discussion in Washington last week that Kim's approach will be to "actually not really giving up anything." At the same time, he'll have "clear demands for the United States to give up things very much in the present" possibly including military exercises, troop deployments and sanctions.
North Korea currently faces United Nations sanctions and separate sanctions from the United States. The UN blocks some imports and exports and has frozen the assets of individuals connected with Pyongyang's nuclear program. The United States restricts the North Korean economy further and targets more individuals.
—CNBC's Huileng Tan contributed to this report.