Minutes after Mr Trump's press conference, the Singapore government invited all accredited journalists to a drinks reception to "thank you for your contributions".

"It's over!" it says. Although it's fair to say that a lot of journalists won't be resting just yet.

Image source, Ministry of Communications and Information

Japanese Prime Minister Shinzo Abe has given his reaction to the Trump-Kim summit - here's what he said:

"I respect President Trump's leadership and effort.

"Chairman Kim's commitment to complete denuclearisation of Korean Peninsula was reconfirmed in a document, which I support as a step towards comprehensive resolution of issues around North Korea.

"I also highly appreciated that President Trump firmly mentioned abducted Japanese citizens in the meeting. I thank him for raising the issue clearly.

"I will talk to the president on a phone later.

"Japan will commit to resolve issues around North Korea, such as abduction, nuclear and missile, in co-operation with US, South Korea, China, Russia and international society."

While many analysts are trashing the Trump-Kim summit and accusing the US president of making concessions with little in return, Rüdiger Frank of the University of Vienna takes the opposite view.

Trump has "saved the process" by taking it "one baby step at a time", he says.

Donald Trump has just given a long press conference to journalists in Singapore. A quick recap:

• He said he would be ending "war games" - joint military exercises the US holds with South Korea, which North Korea describes as a preparation for war. Mr Trump also described the military exercises as too expensive. The South Korean government has said it is currently not clear what Mr Trump's intentions are.
• He said the US would not lift sanctions on North Korea until it made progress on denuclearisation. He said Mr Kim had told him North Korea was destroying a major engine-testing site used for missiles. However, the details had not all been worked out because there was not enough time.
• Human rights in North Korea were discussed, he said, adding that "it's rough" in North Korea, but also "rough in a lot of places".
• Mr Trump said Kim Jong-un had agreed to return the remains of US soldiers in North Korea.

This is what North Koreans have been seeing on TV so far today.

"It's been a long time since I've taken it easy," he says.

Of the agreement he signed with Kim, he says: "Congratulations everybody. To me it's a very important event in world history. I want to get it completed."

"If you don't get the ball over the goal line, it doesn't mean enough," he adds.

When asked whether he has a recording of his conversation with Mr Kim, Mr Trump says there are probably some notes, but he's not sure if it was recorded.

But he says that's OK, "because I have one of the greatest memories of all time".

A South Korean journalist asks Mr Trump what he'll say to South Korean President Moon Jae-in.

Mr Trump describes Mr Moon as a "very fine gentleman. He'll be very happy when he hears... I've already sent word to him about what happened".

He says he has sent him the document he and Mr Kim signed, and that he wants both China and South Korea to be involved in the process.

A journalist asks Mr Trump what he is prepared to do if Mr Kim fails to follow through on his promises.

Mr Trump replies: "No I think he'll do it - I really believe it... I think honestly he's going to do these things. I may be wrong. I may stand before you in six months and say 'hey I was wrong'".

He jokes: "I don't know if I'll admit that but I'll find some kind of excuse," to laughter from the press room.

Mr Trump has talked at length about his uncle, a nuclear expert, at the press conference.

Trump is talking about the economic potential he sees in North Korea. He says he has seen "great beaches" in the background of footage of North Korea's military drills.

"I explained to them you could have the best hotels in the world," Trump says.

"Think of it from a real estate perspective," he adds.

Image source, N Korea TV

From BBC Monitoring:

Until a short while ago, North Korean state television was showing an animation feature - educating children to follow traffic rules - even as US President Trump addresses a long news conference, giving details of his summit meeting with Kim Jong-un.

State TV is yet to show any footage of today’s summit in Singapore.

A reporter asks how North Korea will foot the bill for denuclearisation.

Mr Trump replies that he expects South Korea and Japan will be prepared to help them "very greatly".

He also says he wants "significant improvement" on the human rights situation before sanctions are removed.

A reporter asks: "How do you ensure North Korea is not all talk and no action?"

Mr Trump replies: "Can you ensure anything? You can't ensure anything."

"I think he [Kim] wants to make a deal." He says Mr Kim's intention to make a deal is the most important thing.