They've traded insults -- the young North Korean supreme leader calling the 71-year-old American president a "dotard," "mentally deranged," and a "frightened dog" -- and the billionaire businessman and reality television star calling the 30-something dictator "short and fat," "Lil' Rocket Man" and "a sick puppy."
But at some point in May, President Donald Trump and Kim Jong Un may meet face to face, share a handshake and sit down to talk.
How on earth did the U.S. president who promised "fire and fury" raining down on Pyongyang come to planning a meeting with the leader of the world's most rogue state, arming itself with nuclear weapons?
Trump's acceptance of Kim's invitation has shocked the world -- another surprising move by a president who defies norms continuously and seems to make policy on the fly, whether or not his advisers or Trump himself are prepared.
"We are here through a combination of happenstance, impulsiveness on the part of the president of the United States, a little bit of strategy, and a little bit of luck," Michael Fuchs, who served as Deputy Assistant Secretary of State for East Asian and Pacific Affairs in the Obama administration, told ABC News.
HOW WE GOT HERE
For Kim, part of this is simply about what his country needs -- fuel. The international sanctions are really beginning to bite, a State Department official told ABC News, particularly at the end of a brutally cold winter.
Whether Kim is looking for a break from them or using talks to stall and bide time is unclear, but the pain is a factor in his new willingness to engage, analysts say.
But North Korea has also long sought a meeting with the American president. Given its isolation, the country has sought legitimacy and respect on the world stage, in part by assembling a nuclear arsenal and demanding the world recognize it.
Such a meeting would be granting them recognition by the U.S. -- a propaganda coup for Kim to flex in front of his people. That is, in large part, why no sitting U.S. president has done it, so far.
In fact, then-Senator Barack Obama, the Democratic nominee for president, was pilloried for saying he would meet with the leaders of rogue states like Iran and North Korea without preconditions during the campaign.
"Sorry, but only one thing will work!" the president tweeted.
But those were deals without Donald Trump at the table, and what draws Trump to the table is the notion that his "Art of the Deal" negotiating skills would make the difference.
At times, candidate Trump made similar comments to Obama's, telling Reuters in May 2016, "I would speak to [Kim]. I would have no problem speaking to him."
But even further back, he said on NBC's "Meet the Press" in 1999 that he'd "negotiate like crazy, and I'd make sure that we try to get the best deal possible ... Wouldn't it be good to sit down and really negotiate something?"
Shortly after the announcement Thursday, the White House reiterated that line of thinking, with a senior administration official telling reporters, "President Trump has made his reputation on making deals ... It makes sense to accept an invitation to meet with the one person who can actually make decisions instead of repeating this sort of long slog of the past."
HOW TRUMP'S DECISION IS VIEWED
While North Korea is finally getting its meeting, the U.S. is getting nothing in return other than Kim's word to the South Korean delegation that he is interested in denuclearization and will halt nuclear and missile testing until after talks.
To critics, that's caving in, without getting any goods.
"It is difficult to conceive of a higher currency in the diplomatic realm than a first-time U.S. [president] meeting with a North Korean leader -- yet Trump spent that currency without leveraging any concessions from Pyongyang," Bruce Klingner, a senior fellow at the conservative Heritage Foundation who was CIA division chief for the Koreas, wrote Friday, calling the decision "impetuous."
"When it comes to the North Korean regime, we must verify before we trust," six Republican senators said in a letter to Trump Thursday morning.
One of them -- Cory Gardner, the top Republican on the Senate Foreign Relations Committee's subcommittee on East Asia -- followed up in a Thursday night tweet to specify, "The price of admission for a meeting... must be the complete, verifiable, and irreversible denuclearization of the Korean peninsula."
So far, it's unclear if North Korea is really agreeing to that. The White House said Friday that U.S. national security and intelligence teams were looking into it.
For many Democrats who favor diplomacy, Trump won some accolades for taking a "bold" step -- or what the New York Times editorial board called "sensible."
Gardner's Democratic counterpart on the subcommittee, Sen. Ed Markey, D-Mass., welcomed the dialogue and urged Trump "to see these discussions with Kim Jong-un as the beginning of a long diplomatic process. This meeting is just the beginning of talks between the nations, not a conclusion."
"This is a very good and necessary and long overdue step in the right direction," Fuchs said, before arguing there were huge gaps in the administration's ability to execute on the move.
That's a criticism from plenty of skeptics across the aisle, doubtful of the president's negotiating skills or the administration's preparedness.
Critics point out that all sorts of deal-making has eluded Trump so far. He has not renegotiated any trade agreements: the Paris climate accord or the Iran deal, and he hasn't overseen any major legislative fixes on immigration, guns, or health care.
And his big legislative accomplishment -- the tax bill -- received no Democratic votes.
Still, Trump also has his supporters, who argue this moment is different in part because of his credible threat of military force -- the very promises of "fire and fury" that so many were appalled by last August.
"When Donald Trump says I'm prepared to look at military force, he's serious," former U.S. ambassador to the United Nations John Bolten told Fox News Friday. "I think the North Koreans have figured that out."
Bolten, who met with Trump at the White House Tuesday and has advocated a first strike on North Korea, said the chances of a diplomatic solution were low, but, "I think they increase in direct proportion to their fear that Trump might be prepared to use military force."
WHAT COMES NEXT
But now it's the hard part, with State Department and National Security Council staffers scrambling to figure out what Trump should say, what's on the table, and even where the meeting will be.
The confusion was on display less than 24 hours later, after White House Press Secretary Sarah Huckabee Sanders seemed to backtrack: "This meeting won't take place without concrete actions that match the promises that have been made by North Korea."
That was exactly what Republicans like Gardner wanted to hear, but the White House then walked that back too, according to the Wall Street Journal: "The invitation has been extended and accepted, and that stands," a White House official reportedly told the paper.
In Trump's world, it's almost impossible to know if it will happen, until it does. But if they meet, it will be for talks, not negotiations, State Department officials told ABC News.
What's the difference? "Talks would lead to a discussion around a conclusion that we're ready to engage in negotiations," a senior State Department official said. "Negotiations then are a process of writing down on paper what both sides are willing to do, what the commitments are, how those commitments are going to be filled, how they're going to be verified, and who gets what for making those commitments."
In other words, before discussing all that, Kim and Trump have to talk, get to know each other, understand how the other works and what they want, and build a degree of trust. Then, the countries can begin to negotiate the details of a deal.
"Can we at least sit down and see each other face to face? And then we can begin to lay out a map, a roadmap of what we might be willing to work towards," Tillerson said in December, laying out this very path -- before he was shut down by the White House and forced to change his tune three days later.
To do that requires a lot of legwork, from verifying the South Korean delegation's message about what Kim wants, to drafting proposals on what the U.S. is prepared to offer in exchange, and coordinating with American allies South Korea and Japan to ensure a united front.
Some of that may be moot with a free-wheeling president who does what he wants. One State Department official questioned the merits: "The usual stuff like drafting talking points -- Trump would throw out anyway."
Critics on the right and left say that work is also made more difficult by the Trump administration's vacancies, with no U.S. ambassador to South Korea or Special Representative for North Korea.
But to Trump, "I'm the only one that matters, because when it comes to it, that's what the policy is going to be," as he told Fox News in November.
And that's why he believes he should be the one in the room.
Can he and Kim make a deal? It's possible, in a way. Perhaps a face-to-face meeting clears the air and sets the groundwork for what each side wants and where they'll move.
But a meeting could also come and go and set the stage for something much darker.
"Everyone should be aware that this dramatic act of diplomacy by these two unusual leaders, who love flair and drama, may also take us closer to war," warned Victor Cha, the top Asia adviser on George W. Bush's National Security Council and the one-time leading candidate to be Trump's ambassador to South Korea.
The administration took him out of the running, and hours later, he published an op-ed criticizing it for considering a limited first strike on North Korea.
"Failed negotiations at the summit level leave all parties with no other recourse for diplomacy," Cha wrote Friday.
If the two leaders can't make a deal, how could any underlings be able to?
The hope now rests with Kim and Trump and their ability to hit it off. As Trump tweeted in November, "I try so hard to be his friend -- and maybe someday that will happen!"