(CBS) — President Trump and Kim Jong Un have met for the first time in Singapore, shaking hands against the backdrop of U.S. and North Korean flags level and side-by-side.

Mr. Trump said he thinks it will be a “terrific relationship,” and Kim, through a translator, said North Korea had to overcome a number of “obstacles” to get to this moment.

The stakes are high — the U.S. seeks nothing less than the complete and verifiable denuclearization of the Korean peninsula, and Kim wants to see the sanctions on the North eased.

Mr. Trump and Kim are participating in a one-on-one meeting, with translators only, followed by an expanded meeting including their top advisers and a working lunch. According to the White House, the discussions between the U.S. and North Korea are “ongoing and have moved more quickly than expected.”

The White House says that the United States’ delegation at the larger meeting will include Secretary of State Mike Pompeo, White House chief of staff John Kelly, and National Security Adviser John Bolton.

What time is the North Korea Summit?

Follow Kim Jong Un-Trump summit live updates below:

  • Trump says that, “working together, we will get it taken care of”

    In the expanded bilateral meeting, Mr. Trump said that, “working together, we will get it taken care of.”

    There is no press coverage of the meeting itself.

  • Trump says meeting is “very, very good” so far

    After their one-on-one meeting, Mr. Trump and Kim sat down for an expanded bilateral meeting.

    In the room representing the U.S. are chief of staff John Kelly, Secretary of State Mike Pompeo and national security adviser John Bolton.

    Ahead of that expanded bilateral meeting, Mr. Trump was asked how their summit is going so far.

    “Very good,” Mr. Trump said. “Very, very good. We have a great relationship. Thank you, thank you very much.”

  • Trump and Kim complete first conversation

    After about 35 minutes, at roughly 9:50 p.m., Mr. Trump and Kim emerged from the one-0n-one meeting.

    They are now expected to proceed to an expanded bilateral meeting.

  • Trump and Kim speak, kicking off what Trump says will be a “terrific” relationship

    Mr. Trump sat next to Kim and spoke ahead of their meeting.

    “I feel really great,” Mr. Trump told reporters, adding that it’s his “honor” to meet and he and Kim will have a “terrific relationship.”

    “I feel really great, we’re going to have a great discussion, and I think tremendous success,” Mr. Trump said. “It will be tremendously successful. And its my honor, and we will have a terrific relationship I have no doubt.”

    Kim, through his translator, said there were a lot of obstacles to get to this moment, but they made it.

    Only translators are expected to be in the meeting with Mr. Trump and Kim.

  • Trump, Kim shake hands for the first time

    Mr. Trump and Kim shook hands for the first time just moments after 9 a.m. Mr. Trump did not smile as they shook hands, although Kim was spotted smiling after they greeted.

    They shook hands for several seconds, before walking off towards their meeting together.

  • Trump, Kim have both arrived at summit site

    By 9 p.m. EDT, both Mr. Trump and Kim had arrived at the site of the summit.

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    Kim Jong Un arrives at the Capella Hotel in Singapore for his meeting with President Trump on Tuesday, June 12, 2018. CBS NEWS

  • Trump tweets that top adviser Larry Kudlow suffered a heart attack

    With moments to go before the Trump-Kim summit, the president tweeted that his top economic adviser, Larry Kudlow, has suffered a heart attack and is at Walter Reed National Military Medical Center in Washington, D.C.

    Our Great Larry Kudlow, who has been working so hard on trade and the economy, has just suffered a heart attack. He is now in Walter Reed Medical Center.

  • Kim arrives on island where summit is taking place

    According to the Associated Press, Kim has arrived on the island where the summit will take place in less than an hour’s time.

    At the summit site is a display of American and North Korean flags, where Kim and Mr. Trump are expected to shake hands.

  • Kim leaves his hotel for summit meeting

    Kim has also departed his hotel en route to the summit, with dozens of vehicles making up his motorcade.

    The summit is expected to start in less than an hour.

  • Trump leaves hotel for meeting with Kim

    At just after 8 a.m. local time, Mr. Trump is on his way to the summit site.

    As he departed, Mr. Trump tweeted about a Supreme Court ruling that came out hours before.

    “Just won big Supreme Court decision on Voting! Great News!” Mr. Trump tweeted.

    Just won big Supreme Court decision on Voting! Great News!

    — Donald J. Trump (@realDonaldTrump) June 12, 2018

  • A live look at Trump and Kim’s hotels as they prepare to depart for the meeting

    Cameras are stationed outside the hotels where Mr. Trump and Kim are staying. They’re expected to depart their respective locations at 8 p.m. ET for the drive to the Capella Hotel, where the meeting will take place:

  • Trump speaks with South Korean and Japanese leaders ahead of summit

    The White House says the president spoke on the phone with South Korean President Moon Jae-in and Japanese Prime Minister Shinzo Abe on Monday ahead of the summit.

    Here’s how the White House describes the call with Moon:

    President Donald J. Trump spoke yesterday with President Moon Jae-in of the Republic of Korea to discuss recent developments ahead of today’s summit with North Korea. The two leaders vowed to continue their close coordination following President Trump’s meeting with North Korean leader Kim Jong Un in Singapore.

    And with Abe:

    President Donald J. Trump spoke yesterday with Prime Minister Shinzo Abe of Japan. The two leaders discussed recent developments ahead of today’s summit with North Korea and agreed to consult closely following the meeting.

  • What’s at stake at the meeting?

    Reporting from Singapore, CBS News chief White House correspondent Major Garrett has a look at what’s at stake for both the U.S. and North Korea at the summit on tonight’s “CBS Evening News“:

  • Pompeo departs for summit meeting

    The secretary of state is en route to the summit meeting, which is set to get underway in under two hours:

  • Trump tweets at “haters & losers” before meeting

    A few hours before his meeting with Kim, the president acknowledged in a tweet that preliminary meetings “between staffs and representatives are going well and quickly,” adding, “but in the end, that doesn’t matter. We will all know soon whether or not a real deal, unlike those of the past, can happen!”

    Then, he slapped at his critics, “the haters & losers” who say that “the fact that I am having a meeting [with Kim] is a major loss.” He argued, “We have our hostages, testing, research and all missle [SIC] launches have stoped [SIC], and these pundits, who have called me wrong from the beginning, have nothing else they can say! We will be fine!”

  • What is success for the North Korea summit?

    Pompeo told reporters on Monday that if diplomacy does not move in the right direction after Tuesday’s talks, pressure will be ratcheted up on the North Korean regime. “We will see how far we get,” Pompeo said of the negotiations.

    Pompeo also emphasized that the U.S. has its eyes open, since it has been “fooled” before during prior attempts to reach peace in the region. He says that the “v” – verification -matters most.

  • What’s up for discussion?

    Both Mr. Trump and Kim are expected to largely focus their discussion on Tuesday around the denuclearization of the Korean Peninsula. Pompeo told reporters on Monday that the U.S. is prepared to offer “different, unique” security assurances to North Korea.

    “We’re prepared to take what will be security assurances that are different, unique than have been provided – than America has been willing to provide previously,” Pompeo said. The secretary added that he’s hopeful the summit will set the conditions for future productive talks and a potential framework for work towards denuclearization.

    The president told Prime Minister Lee Hsien Loong of Singapore on Monday that he thinks “things could work out very nicely” during Tuesday’s talks.