Trump labelled the North Korean leader "Little Rocket Man" in a speech to the UN General Assembly. The site of the historic talks was a matter of intense speculation before the US President announced on Twitter it would occur here in Singapore, the flashy Southeast Asian city-state that has eagerly accommodated the spectacle.
ELISE HU, BYLINE: Hey there.
Trump then placed his hand on Kim's back as they exchanged small talk with their two translators by their side. Meanwhile, Mr Kim has called Mr Trump "mentally deranged" and a "dotard". But in the evening, he left the St Regis hotel and visited the Flower Dome at Gardens by the Bay with Singaporean Foreign Minister Vivian Balakrishnan.
She is Kim Jong Un's younger sister and is thought to be in her late 20s or early 30s. Trump had earlier tweeted about "excitement in the air!"
Trump and his advisers have said the USA would accept nothing less than full denuclearization before sanctions against the North are lifted, and before North Korea can be fully welcomed into the fold of the broader diplomatic community.
HU: The key negotiator for the North Koreans on American issues is a woman named Choe Son Hui.
During a quarter-century of on-off negotiations, human rights have played second fiddle for US administrations seeking to ameliorate the threat posed by the North's nukes, and there's a reason.
Last year, it would have been a rare sight to see a North Korean flag flying anywhere in Asia.
North Korea is one of the most secretive countries in the world-so secretive that it earned the nickname "hermit kingdom". And it was shortly after that that Trump briefly withdrew from this summit, which, of course, now is back on.
The North Korean leader has also said he now wants to focus on building the country's economy - and wants sanctions relief and worldwide investment.
In September previous year Trump took to Twitter amid an ongoing spat with North Korean policy makers, calling Kim Jong Un a "madman".
North Koreans have always wanted a meeting with a USA president, just no previous administration was willing to do this kind of meeting unless it came with a substantive commitment or concession on denuclearization.
But, as it stands now, North Korea is still a dictatorship, having been led by one family since September 9, 1948. And Secretary of State Mike Pompeo briefed reporters today. In question is Pyongyang's precise commitment to nuclear disarmament, and the security guarantees the United States is willing to offer in return.
"We both want to do something. We will all know soon whether or not a real deal, unlike those of the past, can happen!" There were no specifics on this, but that will be a question that the allies will certainly be interested, especially the allies of South Korea and Japan.
SHAPIRO: Will you just briefly look ahead to what comes after this summit? Where does this go from here? In the pursuit of these objectives, Kim's night out with Balakrishnan is more than just a surreal moment in global diplomacy.
The other carrot for Kim is a possible loosening of punishing UN Security Council sanctions but here too there is discord, with Washington saying sanctions can end only when denuclearisation is complete and Pyongyang wanting "phased" relief as they make progress towards that goal.
Alluding to the North's concerns that giving up its nuclear weapons could surrender its primary deterrent to forced regime change, Pompeo told reporters that the United States was prepared to take action to provide North Korea with "sufficient certainty" that denuclearization "is not something that ends badly for them".