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What we know so far
US President Donald Trump and North Korean leader Kim Jong-un have met.
The men have spoken privately, and then with advisers by their sides.
Trump revealed before the meeting adviser Larry Kudlow suffered a heart attack.
Trump commited to providing security guarantees while Kim reaffirmed his commitment to denuclearisation.
Trump agreed to stop the war games with South Korea and North Korea will destroy a missile testing site.
8.54pm on Jun 12, 2018
Trump has flown out of Singapore after historic summit with Kim Jong-un
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US President Donald Trump has waved a final, triumphant goodbye while boarding Air Force One to fly home to the United States, following today's historic summit with North Korea leader Kim Jong-un and marathon hour-long press conference afterwards where he faced questions on the content of the joint statement the paire signed.
Thanks for tuning in to our live blog of today's events. It's a wrap!
Julie Bishop hails Trump-Kim summit a 'breakthrough'
By Latika Bourke
Australia could offer experts to help assess whether North Korean dictator Kim Jong-un is making good on his promise to Donald Trump to destroy his nuclear weapons capability.
Speaking just minutes after President Trump wound up a marathon press conference in Singapore after signing a document with Kim, Australia's Foreign Minister Julie Bishop said the summit was "a breakthrough".
Julie BishopAAP
"This is the first positive development we've seen involving North Korea in over a decade," she told the ABC.
"We're cautiously optimistic but of course the test will be verification of the denuclearisation."
The rhetoric was positive but Trump-Kim agreement may be fantasy
By Peter Hartcher
Kim Jong-un told Donald Trump at the outset of their summit that many people would see their meeting as "a form of fantasy ... from a science fiction movie."
This, no doubt, has appeal for Trump, who wrote in his book The Art of the Deal that "I play to people's fantasies".
U.S. President Donald Trump and North Korea leader Kim Jong Un walk from their lunch at the Capella resort on Sentosa Island Tuesday, June 12, 2018 in Singapore. (AP Photo/Evan Vucci)AP
Their initial meeting appeared to proceed smoothly but the question is whether these two leaders are actually working to remove a nuclear threat or just advancing a fantasy for their mutual political benefit.
Their rhetoric was positive. A "good prelude to peace," according to Kim. And "better than anybody could have expected," according to Trump. He praised Kim as a "very worthy, very hard negotiator".
And the words of their joint declaration suggest that this is true, because they contain no actual concession from the North Korean leader on the central issue - his regime's nuclear weapons.
What Donald Trump and Kim Jong-un's body language said
By Josh Dye
It was the unprecedented diplomatic meeting for which the world was waiting.
After decades of frozen relations and a diplomatic stand-off dating back to the Korean War, history was made when a sitting US President and a North Korean leader met face-to-face for the first time on Tuesday.
What meaning can we take from the language of this handshake?AP
Relations thawed in the steamy climes of Singapore, the city state with a reputation for neutrality. The two unpredictable leaders - Donald Trump and Kim Jong-un – came together for an historic handshake in front of dozens of cameras and millions of viewers.
So when the moment finally arrived, how did both men perform on with the eyes of the world watching?
Trump speaks: 'Adversaries can indeed become friends'
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The U.S. President has spoken enthusiastically for about an hour about his meeting with North Korean leader Kim Jong-un and the joint statement they signed together, taking questions from not-so-enthusiastic reporters. Here's some of the major points.
Donald Trump answers questions about the summit with North Korea leader Kim Jong-un.AP
On his new friendship with Kim Jong-un:
"My meeting with Chairman Kim was honest, direct and productive. We got to know each other well in a confined period of time, under a very strong, strong circumstance."
"As history has proved over and over again, adversaries can indeed become friends."
"There is no limit to what North Korea can achieve when it gives up its weapons and embraces commerce."
"Chairman Kim has the chance to seize an incredible future for his people. Anyone can make war but only the most courageous can make peace."
What is and isn't in the joint statement?
"Chairman Kim and I just signed a joint statement in which he reaffirmed his commitment to complete denuclearisation of the North Korean peninsula."
"Chairman Kim has told me North Korea has already destroyed a major missile engine testing site. That's not in the signed document, we agreed to that after it was signed."
"We'll be stopping the war games which will save a tremendous amount of money, plus I think it's very provocative."
"Chairman Kim is on his way back to North Korea and I know for a fact that as soon as he arrives he's going to start the process."
On the question of human rights
Trump said North Korea's poor human rights record was discussed, but briefly and the conversation quickly moved on to the repatriation of prisoners, which was "discussed in great detail".
"I believe it's a rough situation over there. We'll be doing something on it. It's rough... it's rough in a lot of places by the way, not just there."
How does Trump know Kim will keep his word?
"Well, can you ensure anything? Can I ensure you're going to be able to sit down properly when you sit down? You can't ensure anything."
"I just know; my instinct, ability or talent, they want to make a deal."
"I think he'll do it, I really believe that otherwise I wouldn't be doing this."
6.43pm on Jun 12, 2018
Trump kicks off news conference with trailer-style highlights reel
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Singapore Summit: The Movie. Would you watch it? Donald Trump's video editors were swift to create a trailer-style highlights reel for the day's action, which he tweeted moments before opening his press conference.
Watch Donald Trump's press conference from the Singapore summit
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After signing what he described as a "pretty comprehensive" document with North Korean leader Kim Jong-un on Tuesday afternoon, Donald Trump fronts the media for a press conference explaining the contents of the agreement.
Watch the press conference below, and read Fairfax correspondent Kirsty Needham's full report from the summit here.
4.56pm on Jun 12, 2018
What's in the letter? Zoom in to read
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While the contents of the document signed by President Trump and Kim Jong-un have not yet been announced, cameras have already captured it for us. All you need to do is zoom in and read for yourself.
The text, revealed after Trump held the letter up for photographers to see, says, "President Trump committed to provide security guarantees to the DPRK, and Chairman Kim Jong-un reaffirmed his firm and unwavering commitment to complete denuclearisation."
The letter does not specify what the commitments are, specifically.
The letter also says US Secretary of State Mike Pompeo will continue dialogue with a North Korean official at the earlier possible date.
"Having acknowledged that the US DPRK summit – the first in history – was an epochal event of great significance in overcoming decades of tensions and hostilities between the two countries and for the opening up of a new future, President Trump and Chairman Kim commit to implement the stipulations in this joint statement."
4.43pm on Jun 12, 2018
Check out my ride: Trump shows Kim Jong-un 'The Beast'
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Just a couple of guys talking cars – while the world watches.
President Donald Trump offered North Korea leader Kim Jong Un a rare glimpse inside the presidential limousine known as 'The Beast' as their historic summit in Singapore wound down on Tuesday.
After meetings and a working lunch, Trump and Kim were spotted approaching Trump's hulking black limousine, adorned with an American flag. Trump gestured to the car and then a Secret Service agent opened the right passenger door.
Kim could be seen smiling as the two stood chatting and Kim peeked inside.
While there was initially some confusion about what the leaders were doing, it quickly became clear that Trump was making a classic alpha male move: showing Kim his ride.
Trump had said before leaving for the summit that he would be able to tell within minutes whether he'd be able to strike a deal with Kim to dismantle the North's nuclear program.
AP
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4.20pm on Jun 12, 2018
Kim Jong-un's motorcade leaves the island
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With the ink barely dry on the letter he signed with Donald Trump, its contents still unknown, Kim Jong-un's motorcade has left Sentosa Island.
It's unclear however whether Kim was in the car, or stayed behind at the Capella hotel.
Kim had been due to fly out of Singapore at 2pm, local time, with Trump departing later in the evening, but the two men are now expected to hold a press conference at 2.30pm, local time (4.30pm AEST). Stay tuned.