The summit is on Singapore's Sentosa Island and is the first meeting between a North Korean leader and a sitting United States president. Kim spent most of the day in his room at the St. Regis hotel before taking a city tour in the evening, while Trump had only one outside meeting with Singapore Prime Minister Lee Hsien Loong.
The two leaders will have a "one-on-one" meeting - accompanied by translators - before wider talks with their top aides. Whatever people feel about Trump and Kim, the stakes on the Korean Peninsula are so enormous that all should be ready to herald the achievement of even imperfect progress in reducing the risks of further nuclear proliferation and war there.
Police and onlookers were also seen gathering outside the Marina Bay Sands hotel, which resembles a giant surfboard perched on three columns at the mouth of the Singapore River.
During a recent visit to North Hwanghae province, CNN spoke to a 38-year-old farmer who said she wanted to visit the United States to see what the country that is "harassing Korean people so much (and) sanctioning our economy" looks like up close.
The Korean Central News Agency said issues of mutual concern, related to the "changed era", will be on the agenda at the summit, including bilateral relations, peace and denuclearization.More news: Trump says does not endorse G7 communique, after 'weak' Trudeau comments
But Pyongyang is demanding as yet unspecified security guarantees and the end of what it calls a "hostile policy" towards it, and has not made clear what concessions it is offering over the nuclear arsenal it calls its "treasured sword" to defend against a USA invasion. "If diplomacy does not move in the right direction ... those measures will increase".
He would not say whether that included the possibility of withdrawing USA troops from the Korean Peninsula, but said the US was "prepared to take what will be security assurances that are different, unique, than America's been willing to provide previously".
Trump has signaled openness to establishing a USA embassy in Pyongyang, according to a report from Axios, which could signal a pathway toward normalizing relations.
Kim's bodyguards were also spotted running alongside the vehicle after he arrived in Singapore.
Trump arrived in Singapore on Sunday after a blow-up over trade with other members of the Group of Seven major industrialised nations in Canada.
- North Korean and American delegations met at the Ritz Carlton., not once, but twice.
North Korea tends to keep its official government commentary on the pages of Rodong Sinmun, which routinely threatened nuclear annihilation of the American mainland previous year.More news: Nigel Farage’s Explosive Row With Caller Over Alleged Russian Collusion
The summit capped a dizzying few days of foreign policy activity for Trump, who shocked USA allies over the weekend by using a meeting in Canada of the Group of Seven industrialized economies to alienate America's closest friends in the West. Lashing out over trade practices, Trump lobbed insults at his G-7 host, Canadian Prime Minister Justin Trudeau.
Acknowledging the wide strategic and ideological divisions between the United States and the DPRK, Robert Kelly, a political science professor at South Korea's Pusan National University, said, "My expectation is that the summit will result in some small improvements, and then lead to a process that takes six months or a year".
The topics on the table at the Kim-Trump summit have remained largely a mystery. Traffic was held up in the steamy midday sun and scores of bystanders were penned in by police when Trump went to meet Lee.
The last-minute change of schedule came as both sides finalized preparations for the meeting.
The pair promised in the document to "build a lasting and stable peace regime" on the Korean Peninsula and to repatriate remains of prisoners of war and those missing in action during the Korean War. None of this would happen immediately, but neither would North Korea offer to give up its nuclear weapons program up front.
The president acknowledged that US intelligence into the North Korean nuclear stockpile is limited, "probably less there than any other country", he said. After greeting each other - an image sure to be devoured around the world - the two leaders planned to sit for a one-on-one meeting that a USA official said could last up to two hours, with only translators joining them. He described it as a "get to know you plus" meeting. Broadcast coverage of the event has been non-stop for the last 24 hours. The actual summit, however, will take place at the Capella Resort on Sentosa Island, a popular recreation spot off the southern tip of Singapore.
However, future investment in North Korea would not be without its risks. North Korea may or may not be able to hit Washington with a nuclear-tipped ICBM.More news: New Jersey Blood Services Declares Blood Emergency