"We will have a terrific relationship, I have no doubt," Trump said after the two met one-on-one, joined only by translators, for nearly an hour. Later, following an expanded bilateral meeting and a working lunch that featured beef short rib confit and Häagen-Dazs ice cream, Trump told reporters Kim was "a very talented man," and said he would be willing to invite the North Korean leader to the White House.
Many experts on North Korea viewed Trump's decision to meet one-on-one with Kim a gamble, considering it give Kim's regime something it had long sought — the appearance of a meeting of equals — without a single concession in return.
Even after the two leaders shook hands and departed the summit, it's unclear what Trump or the United States expected to gain from the historic sit-down. What was initially billed as the first step in Kim's willingness to denuclearize turned into what Trump himself described as a "get to know you plus" summit.
Trump held a news conference after meeting with Kim and before departure from Singapore.
Here's how the summit played out overnight:
Trump and Kim Jong Un signed a document acknowledging progress between the United States and North Korea, and pledging to keep momentum alive. Beyond that, the exact details of the agreement weren't made known to reporters covering the summit.
Trump referenced the signing during brief remarks to reporters while walking after lunch with Kim.
Longtime Fox News political analyst Brit Hume appeared less-than-optimistic after seeing Trump's interactions with Kim Jong Un.
"Disconcerting to say the least to see POTUS shaking hands with the thug Kim Jong Un and saying he's 'honored,' " Hume wrote on Twitter.
Hume, responding to a comment by Dan Gainor of the conservative watchdog Media Research Center, said the choice between peace or war was a "false choice."
"There is the option of containment, which worked for half a century with the Soviets," Hume wrote. "It's dangerous and imperfect, but it's not war."
During Trump's one-on-one with Kim, CNN host Chris Cuomo turned to former NBA star Dennis Rodman for analysis of the historic first meeting between the two leaders.
Rodman, who at one time was the only American to have met Kim, choked up when talking about the reaction he received back home after his first meeting with the North Korean dictator.
"When I went back home, I got so many death threats," Rodman said. "I couldn't even go home. I had to hide out for 30 days."
Rodman said President Obama "didn't give me the time of day," when he offered to assist the country regarding North Korea. But earlier on CNN, Obama's former director of national intelligence, James Clapper, said he would have been willing to turn to Rodman for his help.
"I have long been an advocate of involving Dennis Rodman," Clapper said, later praising the former NBA star as being the best source for understanding Kim.
Former Associated Press Pyongyang bureau chief Jean Lee tweeted that the historic handshake between President Trump and North Korean leader Kim Jong Un was both "stunning" and "chilling."
"To see Trump & Kim shake hands is both stunning & chilling. It's a powerful moment that augers a change in the tense US-#NorthKorea relationship," Lee wrote. "But it also legitimizes the path Kim took to get here: Testing #nuclear weapons with potential to wreak unimaginable destruction."
After stepping out briefly on a balcony to greet reporters at the Capella Hotel, Kim Jong Un was overheard describing the summit with President Trump, through a translator: "Many people who will think this as a science fiction movie."
Larry Kudlow, Trump's chief economic advisor and a longtime CNBC host, is recovering from a "very mild heart attack" at Walter Reed National Military Medical Center, according to White House Press Secretary Sarah Sanders.
"Larry is currently in good condition… and his doctors expect he will make a full and speedy recovery," Sanders said in a statement.
On his way to his historic meeting with Kim Jong Un, President Trump broke the news of Kudlow's heart attack on Twitter.
Ahead of their second round of talks, President Trump told North Korean leader Kim Jong Un that he believes "we will be successful."
"We will be successful," Trump told Kim through a translator. "And I look forward to working on it with you. It will be done."
Following his one-on-one meeting with Kim, Trump said his meeting with the North Korean dictator went well.
"Very good. Very, very good," Trump told reporters. "Excellent relationship."
After sharing a historic handshake with Kim Jong Un, President Trump told reporters that he and his North Korean counterpart "will have a terrific relationship, no doubt."
Trump and Kim are scheduled to speak one-on-one for an hour with translators, followed by an expanded bilateral meeting scheduled to begin at 10 a.m. local time (10 p.m. Philadelphia time).
Just 20 minutes ahead of his historic meeting with Kim, Trump tweeted that Larry Kudlow, his chief economic advisor and a longtime CNBC host, has suffered a heart attack back in Washington, D.C. Kudlow's current health status is unknown.
"He is now in Walter Reed Medical Center," Trump wrote on Twitter.
Kudlow's wife, Judith, told the Washington Post's Robert Costa that her husband was "doing fine," adding that the doctors at Walter Reed are "fabulous."
Both President Trump and Kim Jong Un have arrived at the Capella Hotel, where the summit between the two leaders will take place. A U.S. official told CNN's Jeff Zeleny that Trump's welcome to Kim will be "warm, polite, respectful" — but won't include a big smile.
As he departed his hotel around 8 a.m. local time, Trump sent another tweet, this time about a Supreme Court ruling that upheld Ohio's method of purging names from voter rolls.
"Just won big Supreme Court decision on Voting! Great News!" Mr. Trump tweeted.
Following his historic summit with Kim, Trump will sit for an interview with friendly Fox News host Sean Hannity at the Capella Hotel on Sentosa Island, where the summit is taking place. Hannity hosted his syndicated radio show on Monday from his hotel in Singapore.
It's unclear when the interview between Hannity and the president will take place. Trump is scheduled to speak to reporters at 4 p.m. local time (4 a.m. in Philadelphia) before departing the hotel.
The interview will air on Hannity's show on Fox News Tuesday night at 9 p.m.
Tuesday morning Singapore time, just hours before his historic summit with Kim, Trump responded to "haters & losers" in a typo-filled tweet who have expressed skepticism about the possibility of obtaining any meaningful concessions from the North Korean leader.
In an earlier tweet, sent around 5:30 a.m. Singapore time, Trump said meetings are "going well and quickly."
President Trump moved up his departure from Singapore after his North Korean counterpart did the same, according to Bloomberg News.
Kim will now leave Singapore at 4 p.m. local time (4 a.m. East Coast time) after his meeting with Trump. The president, who initially said the summit could go one for "two [or] three" days, will leave the summit at 6:30 p.m. and fly home at 7 p.m. local time Tuesday, according to his public White House schedule.
"There's a sense that the administration has a feeling that this may not be as big as they want it to be, and doesn't want to look like they've set up themselves for failure," Associated Press reporter Josh Lederman said on Fox News Tuesday evening.