US President Donald Trump and North Korean leader Kim Jong-un sign an agreement in Singapore
North Korea "commits to work towards the complete denuclearisation of the Korean peninsula" but analysts say it has not made specific commitments
Mr Trump later defends what he has achieved and stuns observers by saying the US will stop war games with South Korea that infuriate the North
He says Mr Kim agreed to destroy a "major missile engine testing site" and that sanctions won't be lifted until progress is made on denuclearisation
The summit is the first time a sitting US president has ever met a North Korean leader
Image source, AFPJapan is nervously watching from the sidelines. Seen as an enemy by Pyongyang and within reach of its missiles, Tokyo has high stakes in the game. PM Shinzo Abe met Mr Trump several times to push some of Tokyo’s points onto the agenda; most importantly the release of Japanese citizens abducted by the North.
Image source, ReutersThe biggest outside player, undoubtedly, is Beijing.
China has for decades been North Korea’s main economic backer and there’s a good chance any deal Mr Kim reaches with the US will need tacit endorsement from Beijing.
Ahead of the inter-Korean talks, Mr Kim suddenly showed up in Beijing for a state visit - his first overseas trip since taking office. That suggests he still needs to align his diplomatic moves with Beijing. He also came to Singapore on a Chinese plane, travelling via China, on his way to Singapore.
In case you've forgotten, dotard was the phrase used by Mr Kim to describe Mr Trump.
Here's more from Dennis Rodman, who just appeared on CNN to share his joy at seeing his friend, Mr Kim, meeting Mr Trump.
"I am not in this for no money... This is not about Dennis being the greatest person in the world. It has nothing to do with that. I just wanted to see it get done so we all can live good together - no more hatred.
"The one thing I always say about him [Kim Jong-un] is he is more like a big kid, even though he is small, .... He loves to have a good time."
Ahead of today, South Korean President Moon Jae-in has, in a series of tweets, declared his hope for the summit to be recognised as a “historic milestone from war to peace”.
However, he’s also expressed a dose of realism as to how quickly things can be achieved, saying that “ the nuclear issue could not be completely solved by one summit but could “ take one year, two years or even longer for a complete resolution".
A retired NBA star, Dennis Rodman has been to North Korea several times. He and Kim Jong-un say they are friends. Mr Kim is a massive basketball fan and, odd as it may seem, Rodman has come to Singapore for the summit.
His visit is paid for by Potcoin - a cryptocurrency used by the marijuana industry.
What's different from Kim's first handshake with Korean President Moon and U.S. President Trump?
You can apparently see that the Moon-Kim handshake was more dramatic with Moon stepping over the line into the North.
The Trump-Kim handshake was more formal - with less drama - but Koreans did note that Trump had a "warm smile" on.
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This was Mr Trump and Mr Kim as they walked into their private talks.
Whatever you make of this day, history really has been made.
South Koreans cheer as they watch the historic moment President Trump shook hands with Mr Kim. It's not dissimilar to the reaction when their own president shook hands with Mr Kim.
Image source, Getty ImagesLittle rocket man? Sick puppy? Some of Mr Trump's past names for Mr Kim might not go down too well today.
BBC News Korean editor Su Min Hwang took at look at what options the US president has, as they sit in that library for their tete-a-tete.
What should Donald Trump call Kim Jong-un?
Over in South Korea, President Moon Jae-in was also watching that historic handshake.
"There is massive distrust on the part of the North Koreans especially," says the BBC's Rupert Wingfield-Hayes, who is in Singapore. "President Trump is going have to win Kim Jong-un over to the idea that he can trust him."
Image source, AFPBut not North Korea.
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Kim Jong-un is the top search keyword on South Korea's biggest web site Naver. "Kim Jong-un's age" is ranking third, while "Trump" is sixth.
The moment when Donald Trump and Kim Jong-un shook hands
Two key quotes from that brief press conference.
Donald Trump: "I feel really great. We’re going to have a great discussion and I think tremendous success. It will be tremendously successful. And it’s my honour and we will have a terrific relationship I have no doubt."
Kim Jong-un (via translator): "Well it was not easy to get here. The past... and the old prejudices and practices worked as obstacles on our way forward. But we overcame all of them and we are here today.
Mr Trump and Mr Kim can be seen here making their way to the library at the Capella for their private conversation.
Image source, ReutersNorth Korea analyst Ankit Panda tweets: