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, ePAThis was history-in-the-making part one.
Kim Jong-un shaking hands with South Korean President Moon Jae-in back in April. These are two leaders of countries which have, technically, never ended the Korean War. Their talks on ending that war are ongoing.
The BBC's Laura Bicker is at a Korean community centre in Singapore.
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A smiling Mr Kim. Less so from Mr Trump.
But a firm handshake.
Here's a clearer photo of that handshake.
Image source, AFPThe leaders spoke briefly to the press - all smiles from Kim Jong-un - and then went into their private conversations.
It appeared cordial, but not overtly friendly. Nothing like the bear hugs Mr Kim exchanged with his South Korea counterpart Moon Jae-in only weeks ago.
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Kim Jong-un and Donald Trump are sitting side by side.
Mr Trump says he believes they will have a "terrific relationship".
The idea of a US president and a North Korean leader shaking hands in a friendly manner would have been unthinkable only months ago.
This is a truly historic moment. What does it mean for the world? That is yet to be seen.
But will these all get talked about in a 45-minute chat?
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People are glued to their TV screens - waiting to catch a glimpse of the moment that Mr Trump and Mr Kim finally meet.
Image source, EPAThe US president and the North Korean leader are both at the five star Capella hotel.
They will meet for a very short time, just the two of them and their translators.
They will then bring in their aides.
We don't know what they'll talk about and we don't know what will come of today.
US President Donald Trump has pulled up at the hotel.
North Korea's nuclear site destruction: What does it mean?
To prove that it’s serious about denuclearisation, North Korea recently blew up its one known test site.
A select group of foreign journalists were invited to witness the spectacle but there are doubts whether it really meant anything. Pyongyang might not need any more tests - as it already has nuclear weapons - or might resume testing elsewhere.
Image source, Rodong SinmunBecause the world has - with notable exceptions - agreed that there should be no new nuclear states and that the existing ones will not use theirs.
North Korea in particular is widely considered not to be responsible enough to have nuclear weapons - after all, it does keep threatening to use them. Its nuclear programme has always been worryingly secretive, and there is real fear that if the government collapsed, the nukes could fall into the wrong hands.
North Korea has conducted six underground nuclear tests. What did they achieve?
Kim Jong-un is at the Capella for the summit.
This summit animation has been shared on Twitter and is also making its rounds on Instagram.
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For a long time, it was very unclear whether today would happen. Washington and Pyongyang quarrelled over whether Libya’s denuclearisation was a legitimate model for North Korea, and on 24 May, Mr Trump called off the talks, blaming North Korea. Pyongyang wooed Washington with visits and a personal note from Mr Kim, and eventually things were back to the original schedule.