U.S. President Donald Trump and North Korean leader Kim Jong Un met face-to-face Tuesday morning for their highly anticipated summit. After hours of talks, the U.S. president said he was heading toward "a signing" with Kim, but there was no immediate indication of what sort of agreement would be signed. The summit began with the two men briefly shaking hands and taking a photo side-by-side, then moving to another room, where they sat and made brief statements for the press. "We're going to have a great discussion and, I think, tremendous success. It will be tremendously successful. And it's my honor," Trump said. "We will have a terrific relationship — I have no doubt," the president added. For his part, the North Korean leader said, "It was not easy to get here. The past worked as fetters on our limbs, and the old prejudices and practices worked as obstacles on our way forward. But we overcame all of them, and we are here today," according to a translation provided by the White House. Trump responded: "That's true." Following those comments, the two leaders began what was said to be a one-on-one meeting, with only translators in attendance.

North Korea's leader Kim Jong Un (L) shakes hands with US President Donald Trump (R) at the start of their historic US-North Korea summit, at the Capella Hotel on Sentosa island in Singapore on June 12, 2018. Saul Loeb | AFP | Getty Images

They then made a brief appearance together at a balcony exposed to cameras, and then headed into a larger bilateral meeting. With delegation members on opposing sides of the table, Trump delivered another message to Kim. "Mr. Chairman, it's a great honor to be with you, and I know we'll have tremendous success together and we'll solve a big problem — a big dilemma — that until this point has been unable to be solved, and working together we'll get it taken care of," Trump said before reaching for another handshake with his North Korean counterpart. After hearing Kim's response, Trump added: "We will solve it, we will be successful, and I look forward to working on it with you. It will be done." Later in the day, the two men walked out of the meeting together, and Trump addressed the media. "It's going great. We had a really fantastic meeting, a lot of progress, really very positive. I think better than anybody could have expected — top of the line, really good," the president said. "We're going right now for a signing," he added, walking away from the assembled media.

First such meeting in history

It was the first time that sitting leaders of the countries have met, and it came after years of bluster and threats from Pyongyang — and from Trump — that have raised fears of war. Of note, many analysts have argued that any recent U.S. leader who had wanted to meet with Kim or his father before him could have done so, because North Korea sought the legitimization of such an event. Trump is giving Kim's regime that opportunity, but the U.S. team has also said it is resolute in its goal for Tuesday's summit: North Korea's total and verifiable denuclearization.

American officials have dangled relief from stringent international sanctions or even economic aid if the hermit regime were to acquiesce. Beyond those benefits, North Korea is understood to want guarantees about the future of its autocratic regime and the security of its borders. Washington is hoping the bilateral discussions will be the first of many with Kim's government, eventually leading to the country surrendering its nuclear capabilities. That weapons program has become a threat to neighbors South Korea and Japan — and more recently, even for the U.S. mainland. For decades, Pyongyang has sought to depict the United States as an imperialist aggressor for its role in the Korean War, while simultaneously blaming Washington for North Korea's dire economic condition. The isolated country has long said it's justified in seeking nuclear weapons in light of an "extreme and direct nuclear threat" from the United States. Tuesday's meeting is seen as a diplomatic breakthrough, even if some experts have said the summit is a strategic mistake on Washington's part, since it allows Kim to appear as an equal to Trump.

What will North Korea demand?

Experts predict little in terms of concrete results from the summit. In the past, Pyongyang has said it may denuclearize only if certain conditions were fulfilled. Those include terminating America's military presence in 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. Washington has said its troops in South Korea would not be up for discussion during the Tuesday summit. Such a withdrawal could have major implications for Asia.

President Donald Trump (R) shakes hands with North Korea's leader Kim Jong Un (L) as they sit down for their historic US-North Korea summit, at the Capella Hotel on Sentosa island in Singapore on June 12, 2018. Saul Loeb | AFP | Getty Images