In March, Trump accepted Kim's invitation to meet, breaking with predecessors who had shunned any type of a summit without major concessions from North Korea or multilateral talks that included a host of other Asian countries. And Secretary of State Mike Pompeo sought to keep expectations for the summit in check.
A suite on the 20th floor of St. Regis Hotel, where Kim is staying, costs more than 13,000 Singaporean dollars a night.
Trump has also raised the possibility of further summits.
Kim was accompanied at the meeting by vice-chairman of the Central Committee of the Workers' Party of Korea (WPK) Kim Yong Chol, chairman of the Foreign Affairs Committee of the WPK Ri Su Yong, and Colonel General No Kwang Chol - one of the three promoted in a recent North Korean military shakeup.
Lobster bisque, beef tenderloin and ice cream were on the lunch menu, and there was also an early birthday cake for Trump, who turns 72 on Thursday.
"It is our contribution to an worldwide endeavor which is in our profound interest", he told reporters on Sunday.
Former PM Mulroney predicts Trump rage at Justin Trudeau a passing storm
Trump in Singapore today escalated his war of words with Canada and the European Union in a pair of tweets . His aides took the matter further. "He really stabbed us in the back ". "We went through it".
The two leaders are at the site, with Kim arriving at 8:55 p.m., and Trump showing up five minutes later.
Rodman appeared in Trump's Celebrity Apprentice reality TV show, only to be booted off because he misspelled Melania Trump's name.
But once North Korea conducted an underground test of a thermonuclear bomb last September, Trump began taking Kim more seriously.
Although gaps remain over what denuclearisation would entail, Trump sounded a positive note in a lunch meeting with Singapore's Prime Minister Lee Hsien Loong.
Many analysts have suggested that the discussion about denuclearization means very different things to North Koreans than it does to American officials. Meanwhile, Mr Kim has called Mr Trump "mentally deranged" and a "dotard".
Pyongyang has said it is willing to deal away its entire nuclear arsenal if the United States provides it with reliable security assurances and other benefits.
Trump has blamed past presidents for failing to resolve tensions with North Korea as it has pursued a nuclear program, testing missiles in displays of posturing and provocation.
That's in part because of South Korea's diplomatic outreach to the North, which was highlighted by two summits this spring between the rivals' leaders.
The US president and the leader of DPRK are quite different people.