Image source, AFP

Back to food briefly. Remember that inter-Korean summit in April? Everything was painstakingly choreographed and loaded with symbolism: from the chairs to table diameter to flowers, tree planting and food. This time round? None of that, at least nothing that’s been announced so far. But during his 2016 campaign, Mr Trump said he wanted to eat a burger with Mr Kim.

Not everyone is happy with today's events. It's jarring for many opponents of these two men.

Meanwhile, a minor crisis is brewing in the media centre. Our colleagues over there say the centre has run out of coffee. Everyone was up early so it's not going down well. Is world media coverage about to slow down?

It's fair to say the 3,000 or so journalists here are being otherwise well catered for, if this image of the dessert bar is anything to go by.

South Korea's President Moon Jae-in says he spent a "sleepless night" ahead of the summit, but added that he hoped the summit would "open a new era of complete denuclearisation, peace and a new relationship between South Korea, North Korea and the United States".

US broadsheets have dropped their usually measured tone to blare the history-making moment from Tuesday's front pages.

Singapore has said the cost of hosting this summit is about $20m Singapore dollars ($15m; £11m). That’s mostly going to be security and the cost of hosting the 3,000 or so foreign media personnel who are believed to be in town - the biggest foreign media deployment the city state has ever hosted. Oh, and Singapore is also paying for Kim Jong-un's hotel during the stay.

Here's more of that from our Asia Business Correspondent Karishma Vaswani.

A bit more on John Bolton, and why it was striking to see him sitting opposite Mr Kim here in Singapore.

Mr Bolton was the one who brought up the Libyan model as an example of how North Korea should denuclearise. That did not go down well at all with Pyongyang. The war of words that followed escalated and the summit was even called off by Mr Trump, briefly.

What's the problem with mentioning Libya? A few years after that country agreed to give up its very basic nuclear weapons programme, leader Muammar Gaddafi was toppled by his people and killed in the streets by an angry mob. That is North Korea's worst nightmare so they will never agree to such a deal.

More from our correspondent in Singapore, Rupert Wingfield-Hayes. "What we are seeing here from Kim Jong-un is a very different style, very different from previous North Korean leaders, very different from his father Kim Jong-il."

"But the question on everyone's mind is of course how much of a difference is there in substance. Is this really a man who wants to change his country's stance to the international community?"

"This is fundamentally different from what we have seen before," says BBC correspondent Rupert Wingfield-Hayes. "In the 1990s, the framework agreed on between the Clinton administration and Mr Kim's father was a long protracted negotiation behind closed doors by specialists on diplomacy and disarmament before Secretary of State Madeleine Albright went to Pyongyang."

"This time, it's basically upside down. The two leaders are meeting before much of the details have been worked on by the specialists. So this is rather the beginning of a process."

Barack Obama, Narendra Modi, Xi Jinping - they’re just some of the world leaders who have had orchids named after them upon their visit to Singapore. (Orchids being Singapore's national flower.)

So might we see a Donald Trump or Kim Jong-un orchid? Or simply an orchid marking the joint summit? Possibly.

Image source, Getty Images

Some of the people Mr Kim has brought with him:

Kim Yong-chol: Seen as Kim Jong-un's "right hand man," he went to Washington for summit preparation talks earlier this month, making him the most high-profile North Korean to ever visit the US.

Ri Yong-ho: North Korea's foreign minister. His diplomatic career goes back to the 1990s where he took part in talks with the US.

Ri Su-yong: He previously held the post of foreign minister before it was passed on to Ri Yong-ho. However, he still remains one of the highest-ranking officials in Pyongyang.

Image source, Reuters

On the US side of the table, US Secretary of State Mike Pompeo was sitting beside Mr Trump, with his chief of staff John Kelly on the other side.

And if you look really closely, you can just about see security adviser John Bolton at the very corner of the table.

Remember, it was partly Mr Bolton's comments that nearly threw the summit off course a few weeks ago.

South Korean celebrities are hoping that the historic meeting between Mr Trump and Mr Kim will have a happy ending. "Hope this leads to a good meeting, a good result, like what happened to us," wrote R&B singer Shin Seung-hoon, referring to the recent meeting between Mr Kim and South Korea's president.

"There's going to have to be a give and take between the two sides," Prof Robert Kelly of Busan University in South Korea told the BBC, while talks continue.

"The North Koreans will not give away everything. And even if they give up something they will ask for sanctions relief or they will ask for some aid. And those details will be difficult to work out."

Watching the events from the US is Grace Jo, one of the many North Koreans who has escaped what is widely known to be a brutal government. She's been sharing her thoughts with the BBC's Hugo Bachega in Washington.

"I feel very sorry that human rights are not being discussed. We can’t separate the nuclear issue from human rights issues. They developed nuclear arms while people were dying of starvation, others in prisons."

It's hard to make out exactly what they're saying over the camera clicks in an echoey room.

But analyst Ankit Panda tweets:

And that's it - the private talks are over. The two leaders are now sitting down at a conference table with their teams.

"Nice to meet you, Mr President," Mr Kim said to Mr Trump in English.

Facts about the North Korean leaders are not well known, but there are indicators he is actually fluent in English. Following Dennis Rodman's 2013 visit to North Korea, media reports said the two spoke directly to each other without an interpreter. Mr Kim, of course, spent his school days in Switzerland.

Image source, Reuters

Russia. Historically an ally since the days of the Soviet Union, Moscow has condemned Pyongyang’s nuclear programme but also criticised international sanctions as useless. And while it looked like Russia was going to be sidelined in the latest diplomatic tango, just before the summit, Russian Foreign Minister Sergei Lavrov went to Pyongyang. And guess what: he set up a Kim-Putin summit to take place later this year.