If you’re tuning into the summit now and could do with some background music, you might want to check out some of these Trump-Kim inspired hits.

From K-pop to John Lennon, we’ve got you covered. You’re welcome.

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They may look like the best of friends now, but don't forget that the US and North Korea are technically still at war. The Korean War ended in 1953, but with an armistice - they stopped fighting but have never signed a peace treaty, so it's something of a dormant war. North Korea really wants it to be declared over.

There is speculation that in a few hours we may get some kind of declaration of peace from the two leaders. This would not be a formal peace treaty - that brings huge political implications and would have to involve changes in constitutions, as well as agreement from China and South Korea. But they MAY commit to moving that process forward.

Mr Trump's National Security Advisor, defence hawk John Bolton, has made an appearance - but it appears he's not at the bilateral talks.

It didn’t come up at the previous summit and there’s a big chance it won’t be mentioned this summit - we’re talking about North Korea’s human rights situation.

Issues like forced labour, a lack of religious freedom, prison camps and a huge lack of rights for women plague country - something that's easy to forget in the flurry of diplomatic activity.

You might have heard the word, Yongbyon, a lot. That is the nuclear facility which produces material that could be used in North Korea's nuclear weapons. Any commitment to shut down part of Yongbyon would be seen as a sign of some progress, says nuclear expert Melissa Hanham.

"It's a big place, like any US nuclear lab, and it will take time and effort to close it down. But if they do shut down the two operational reactors there, the North really won't be able to produce plutonium, which is a clear benefit"

But, she cautions, we know of at least two uranium enrichment facilities outside of Yongbyon. So if any agreement does represent a scaling back of Yongbyon "take the win, but remember there are others out there too".

Here's the moment the two leaders of nuclear-armed states who once flung insults at each other liberally and threatened each other with annihilation sat down for their friendly chat.

Mr Kim said people remained sceptical about their meeting "but I'm sure that all of them would be watching the moment that we're sitting together side by side as if they're watching a fantasy movie".

Both the US and North Korean leaders have now stepped behind closed doors again, but here's a recap of what they said before they began talks on the key day of their second summit:

Mr Trump, on denuclearisation: "I've been saying very much from the beginning that speed is not that important to me. I very much appreciate no testing of nuclear rockets, missiles, any of it, very much appreciate it. We just want to do the right deal."Mr Kim, on whether he was confident about a deal: "It's too early to tell, but I wouldn't say I'm pessimistic. For what I feel right now, I do have a feeling that good results will come out."

Image source, Getty Images

North Korea expert Olivia Enos explains why it's vital that North Korea's human rights issues are discussed at this summit.

Mr Kim's sister - Kim Yo-jong - is a member of his trusted inner circle. She made her first international appearance during the Winter Olympics, where she became the first immediate member of the North's ruling family to visit the South since the Korean War.

She's made several appearances since, including at the Trump-Kim summit in Singapore last June - and now here she is in Hanoi.

Christopher Hill told the BBC there had been few signs of real commitment to denuclearisation since the Singapore summit, but that the North Koreans already had their success.

"They’ve broken out of the diplomatic isolation we made a big effort to put them in."

You can watch his interview in full here

Christopher Hill led the US delegation during the six-party talks - a series of lengthy negotiations with North Korea in the 2000s that ultimately collapsed.

Now at the University of Denver, he told the BBC earlier this week that it was "not a lot of fun" negotiating with them.

"You think you have an agreement, you circle back to it - and then you don’t have an agreement."

The one-to-one meeting between Mr Trump and Mr Kim lasted all of 30 minutes - 15 minutes shorter than it was supposed to be.

But according to analyst Ankit Panda, it's probably best not to "make too much of this".

The two leaders have now finished their one-on-one meeting, but will soon be joined by officials for an expanded bilateral meeting.Afterwards, they'll head to lunch at 11:55 local time.

Image source, AFP

Our Koreas correspondent Laura Bicker, who is in Hanoi, tweets:

Here's Mr Trump and Mr Kim, along with US Secretary of State Mike Pompeo who has been a lead negotiator with the North Koreans, in the garden. It's quite chilly outside, but fresh air helps the mind of course.

Image source, Reuters

Kim Jong-un is facing expectations from North Koreans to score a good deal at the summit, as North Korea expert Andray Abrahamian explains. The big deal for him is sanctions, which are holding back his country's development.

After a quick chat, we're now seeing live footage of the leaders taking a walk around the garden with their colleagues and some Vietnamese leaders.

If you’re just joining us and want to catch up, check out our guide with everything you need to know about the Trump-Kim summit.

Image source, Getty Images