(CNN) Donald Trump and Kim Jong Un met Tuesday in front of the world's cameras, against the backdrop of flags of the United States and North Korea.

The leaders approached each other on a red carpet from separate outdoor hallways at the airy and luxurious Capella Hotel on Singapore's Sentosa Island.

When it came time to finally shake hands, the they both flashed guarded smiles. Trump briefly touched Kim's right upper arm, then they turned to face the cameras. The leaders moved off to the side, greeted by two individuals who appeared to be translators.

A camera from above showed them touching each others' arms in a friendly manner, with remarkably relaxed body language considering the magnitude of the moment.

Thumbs up from Trump

In a nearby meeting room, the leaders sat side-by-side. Trump leaned forward with his hands clasped. Kim leaned to his left in a casual manner toward the US President.

Trump spoke first.

"I feel really great, we're about to have a great discussion," Trump said. "I think it will be tremendously successful, and it's my honor and we will have a terrific relationship. I have no doubt."

JUST WATCHED Trump, Kim speak before summit Replay More Videos ... MUST WATCH Trump, Kim speak before summit 01:24

Kim then gave a few words.

"It has not been easy to come to this point. For us the past has been holding us back, and old practices and prejudices have been covering our eyes and ears, but we have been able to overcome everything to arrive here today," Kim said in Korean.

In response, Trump offered Kim a thumbs up. They then reached over to shake each hands, again smiling.

U. S. Donald Trump gives North Korea leader Kim Jong Un a thumbs up at their meeting at the Capella resort on Sentosa Island Tuesday, June 12, 2018 in Singapore.

Private meeting

Trump and Kim's started their summit with a personal meeting, joined only by two translators. It lasted 38 minutes.

The two leaders then strolled through the Capella Hotel. "Excellent relationship," Trump said from the balcony.

As they walked on the colonnade, Kim remarked that many people around the world wouldn't believe what was taking place in Singapore.

"Many people in the world will think of this as a (inaudible) form of fantasy ... from a science fiction movie," Kim told Trump, through a translator.

US President Donald Trump and North Korea's leader Kim Jong Un walk through the Capella Hotel after concluding the first series of talks.

At a large meeting table, Trump and Kim began their second series of talks, this time with advisers including US Secretary of State Mike Pompeo, national security adviser John Bolton, and White House chief of staff John Kelly.

On the North Korean side, Kim was joined by his chief diplomat Kim Yong Chol, Foreign Minister Ri Yong Ho and Ri Su Yong, Vice-Chairman of the Central Committee of the Worker's Party of Korea.

"We will be successful," Trump said to Kim, who sat across the table. "And I look forward to working on it with you. It will be done."

Dennis Rodman gets emotional

Former basketball star Dennis Rodman, who has previously boasted of his role in bringing Trump and Kim together, broke down in tears during an interview CNN's Chris Cuomo.

"It's a great day," said Rodman, who arrived in Singapore overnight. "I'm here to see it. I'm so happy."

JUST WATCHED Rodman gets emotional discussing North Korea Replay More Videos ... MUST WATCH Rodman gets emotional discussing North Korea 02:09

Rodman is in the unique position of having personal relationships with both leaders; he participated on Trump's pre-presidency TV show "The Celebrity Apprentice," and has visited Kim several times in North Korea, calling him "a good friend."

When asked about Kim's politics and past actions, Rodman deflected.

"I'm not a politician," Rodman said. "I don't need to worry about the war stuff, all the stuff that's going on -- I don't know anything about that."

What they ate

Kim and Trump's working lunch featured a mix of Western and Korean dishes.

Options for appetizers included a prawn cocktail with avocado salad, green mango kerabu and "oiseon," a Korean stuffed cucumber.

The menu also featured beef short rib confit, sweet and sour crispy pork with Yangzhou Fried Rice or "daegu jorim," a Korean soy braised cod fish.

Menu for today's working lunch with President Trump and Kim Jong Un: pic.twitter.com/OJlkhuouSR — Kevin Liptak (@Kevinliptakcnn) June 12, 2018

Finally to finish, there was dark chocolate tartlet ganache, vanilla ice cream or "tropezienne," a pastry dessert.

The advisers from the extended talks also attended the lunch, along with a few new additions, including Sarah Sanders, the White House Press Secretary, and Kim Yo Jong, Kim Jong Un's sister and the first deputy director of the Central Committee of the Workers' Party of Korea.

Trump shows off the Beast

After the lunch, as Trump and Kim walked through the grounds of the Capella, they seemed to take a detour, veering toward the road.

Trump stopped briefly to greet Kim's sister, Kim Yo Jong, before the pair continued on to walk alone.

JUST WATCHED Trump shows Kim Jong Un presidential limousine Replay More Videos ... MUST WATCH Trump shows Kim Jong Un presidential limousine 01:46

It seemed Trump wanted to show Kim the US presidential limousine, known as the "Beast."

Trump was seen talking and gesturing at the heavily armored limousine, before Secret Service agents opened the door and the leaders took a peek inside.

Kim, Trump sign 'pretty comprehensive' document

As the summit drew to a close, the pair put pen to paper on what Trump described as a "pretty comprehensive" and "very important document" during a signing ceremony.

JUST WATCHED Trump, Kim Jong Un sign 'historic document' Replay More Videos ... MUST WATCH Trump, Kim Jong Un sign 'historic document' 02:34

Kim, sat alongside Trump at a table where the document was signed , said it was time to "leave the past behind."

"The world will see a major change. I'd like to express my gratitude to President Trump to make this meeting happen," he added.

Trump holds up a document signed by him and Kim on Tuesday.

Photographs of the document indicate the leaders agreed to "work toward complete denuclearization of the Korean Peninsula."

The document also indicates the leaders will endeavor to establish "new US-DPRK relations."

Trump's wide-ranging presser

In a solo post-meeting news conference that lasted over an hour, a buoyant Trump touched upon a myriad of subjects including his confidence in Kim, the status of military exercises with South Korea and what could come next.

When asked by CNN's Jim Acosta if he trusted Kim, the President responded,"I do. I think he wants to get it done." He described the talks as "honest, direct, and very productive."

JUST WATCHED Trump pressed on denuclearization, military Replay More Videos ... MUST WATCH Trump pressed on denuclearization, military 01:21

He also said he would push for North Korea to denuclearize as "fast as it can mechanically," but acknowledged it could take a long time.

Trump also suggested he would be halting joint US-South Korea military exercises, calling them "inappropriate," "provocative" and "expensive," in an apparent concession to North Korea, which has long been critical of the drills.

"Anyone can make war, but only the most courageous can make peace." @POTUS in Singapore at Press conference following the #SingaporeSummit pic.twitter.com/RDzSUnNPtC — Sarah Sanders (@PressSec) June 12, 2018

Trump said he expected to meet Kim again, telling reporters "we'll probably need another summit or meeting" to hash out the next steps.

"We're much further along than I would've thought," he added.