The talks are expected to begin at 9:00am this morning and end at 9:00pm tonight and could even open the way to an official end to the Korean War, which concluded in 1953 with a truce but never a peace treaty. South Korea will not be at the table, nor will China, the North’s most crucial backer.

The summit meeting is the most prominent moment yet in international diplomacy for both Mr. Trump and Mr. Kim. Not long ago, they were better known for threatening each other’s countries with destruction than for peace overtures.

Here’s what has happened so far:

• Both leaders arrived in Singapore on Sunday, Mr. Trump fresh from a clash with American allies at the Group of 7 meeting in Canada, and Mr. Kim with a little travel help from his Chinese allies.

Just hours before the meeting was to begin, American and North Korean officials continued to scramble behind the scenes, searching for areas of agreement on issues that have eluded consensus for decades.

• With thousands of journalists from around the world congregating in Singapore, Mr. Kim and his entourage left his hotel on Monday night, and the media scrambled before catching up with him at another hotel, where he left for a tour of Singapore.