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.
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.
The summit announcement came in March after several months of unprecedented cordial diplomacy between South and North Koreas, which had been adversaries for decades.
The United States, which has substantial presence in South Korea, was on a war footing with the North over Pyongyang’s nuclear and missile programs.
The development resurrected hopes that Trump and Kim could try to find a solution to the crisis on the Korean Peninsula that has escalated over the past year.