Trump on Kim: 'He's a funny guy' and other summit quotes - BBC News
As Donald Trump offers his own post-summit analysis, we break down what he said and why.
This video can not be played To play this video you need to enable JavaScript in your browser. Was the summit a win-win for both countries, or a Kim win?

The handshake has happened, the summit is over, and now Donald Trump is hitting the media circuit - including his first sit-down interview with a major news network other than Fox - to make the case for what he has accomplished.

Because it's Mr Trump, some of what he has to say is head-scratching, other parts will have his supporters smirking or swooning, while many of his critics will be outraged. Here are a few of his key lines - and what they could mean.

"He's got a great personality. He's a funny guy. He's very smart. He's a great negotiator. He loves his people, not that I'm surprised by that."

This was Mr Trump's response when Voice of America's Greta Van Susteren asked what he found surprising about the North Korean leader. He would also tell ABC's George Stephanopoulos that the North Korean people love him back and that they have "great fervour" for their leader.

That the US president says he was not surprised that Mr Kim, who oversees a totalitarian regime that imprisons an estimated 120,000 of its people for political reasons, "loves his people" or that they love him will certainly come as a shock to many human rights advocates.

In fact, the pageantry of the summit, Mr Trump's solicitous manner and his kind words for Mr Kim have already drawn the ire of some of the president's critics - and others who have, in the past, largely held their tongue.

"I think the North Korean flag is a piece of vile filth that stands for the dynastic rule of a racist cult that subjugates, tortures and enslaves its own people," writes National Review senior editor Jonah Goldberg, regarding the display of US and North Korean flags at the summit site. "Ideally it would spontaneously combust when it even touches our flag."

The National Rifle Association's Dana Loesch said she was "not a fan" of having the US and North Korean flags together, "as any sort of equals".

Several reporters pressed Mr Trump on North Korea's record of human rights violations - and whether the president, who described Mr Kim as "talented", should have been more cautious with his language.

"Anybody that takes over a situation like he did, at 26 years of age, and is able to run it, and run it tough - I don't say he was nice or I don't say anything about it - he ran it," Mr Trump said in reply to a question about his praise of Mr Kim. "Very few people, at that age - you can take one out of 10,000, probably, could do it."

That "talented" line provoked a response from Florida Senator Marco Rubio, who ran against Mr Trump for the Republican presidential nomination in 2016.

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"This isn't the past. This isn't another administration that never got it started and therefore never got it done."

Donald Trump, in his press conference, announced that Mr Kim had "reaffirmed his unwavering commitment to complete denuclearisation of the Korean Peninsula". He had also agreed to "vigorous" negotiations to implement the agreement.

Agreements and negotiations have happened in fits and starts for nearly three decades, of course. Mr Trump sees a different outcome because he sees himself differently. He's the consummate dealmaker.

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"My whole life has been deals," he told reporters. "I know when somebody wants to deal, and I know when somebody doesn't. A lot of politicians don't."

Mr Trump has repeatedly criticised his predecessors, saying that they didn't get the job done - but he campaigned on the promise that he would be a different kind of president and would get a different, better result.

It's a view he's not backing away from.

"I think he trusts me, and I trust him."

During the US-Soviet arms disarmament negotiations of the 1980s, President Ronald Reagan coined the phrase "trust but verify".

On multiple occasions on Tuesday, Mr Trump said he trusts Mr Kim - and Stephanopoulos brought the Reagan line up during his interview with the president.

Mr Trump responded that the US and North Korea would be working together and developing "great relationships at different levels".

As for the details? The "trust" has been professed, but the "verify" is yet to be spelled out.

"If I can save millions of lives by coming here, sitting down, and establishing a relationship with someone who's a very powerful man, who's got firm control of a country, and that country has very powerful nuclear weapons, it's my honour to do it."

One of the prime lines of criticisms directed at Mr Trump for participating in the summit is that he is encouraging other rogue regimes to develop their own nuclear weapons so that they can stand on equal footing with a US president.

Mr Trump has shredded an agreement with Iran that was designed to prevent them from acquiring a nuclear arsenal. It is an "honour", on the other hand, for the president to deal with Mr Kim, a "very powerful man" who has "powerful nuclear weapons".

Arkansas Senator Tom Cotton, a Republican who has largely supported the Trump administration, makes the distinction clear.

"Countries like Iran and Cuba and other two-bit rogue regimes don't have nuclear weapons yet," he told radio host Hugh Hewitt. "They can't threaten the United States in that way. Once North Korea had nuclear weapons, once they have missiles that can deliver them to use, I would liken it to past presidents sitting down with Soviet dictators."

Nuclear weapons got North Korea to the table. The big question now is what it will take for the US to convince Mr Kim to give them up.

"I think the initial rhetoric was very important. Frankly, as much as I hated to do it, and as much as some people thought I was doing the wrong thing, I think without that we wouldn't be here."

It was just under one year ago that Mr Trump warned North Korea that its threats against the US would be met by "fire and fury the likes of which the world has never seen".

He'd go on, over the course of the following months, to deride Mr Kim as "little Rocket Man" and disparage the size of his "nuclear button".

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Lines like those had pundits, politicians and analysts expressing shock and concern that the US was on a path to war - and inside reports from the White House of military deliberations and planning did nothing to ease minds.

Now Mr Trump is saying that it was all part of his strategy - a modern-day incarnation of Richard Nixon's "madman" gambit with the North Vietnamese - which he says may have made him look "foolish" but has proven to be effective.

"We will be stopping the war games, which will save us a tremendous amount of money, unless and until we see the future negotiation is not going along like it should."

This nugget was nestled at the beginning of the question-and-answer portion of Mr Trump's post-summit press conference - and it represents a significant concession on the part of the US side. Even using the term "war games" itself comes across as a nod to the North Koreans. Annual US-South Korea joint military training exercises had been a constant source of irritation for the North, which viewed the operations as preparation for war.

Mr Trump is ending them - at least for the moment - and perhaps most noteworthy is that he couched the revelation as a cost-saving step.

That may play well with Mr Trump's base, who rallied around Mr Trump's campaign pledge to spend US resources at home, not abroad - although it does mark a change of tack from the president's boasts of record level of military spending in the latest US budget for a depleted US armed forces.

"Honestly, I think he's going to do these things. I may be wrong. I mean, I may stand before you in six months and say, 'Hey, I was wrong.' I don't know that I'll ever admit that, but I'll find some kind of an excuse."

This line - a president admitting that he may not admit to mistakes - raised more than a few eyebrows, but it's part of what makes Mr Trump so irresistible to his supporters.

They thoroughly believe that all politicians lie, that they all will never admit mistakes, that they all say whatever they think voters want to hear. Mr Trump, at least in their estimation, is being open about it. He is, in effect, letting them in on the joke.

Maybe this is a mistake. Maybe the negotiations will fall apart. Maybe Mr Trump will find some sort of excuse. But, if that happens, he'll do it with a wink and a nod to those who have stood by him through it all.