Donald Trump and Kim Jong-un: Why could the US and North Korea not reach a deal?

US President Donald Trump and North Korean leader Kim Jong-un have met for talks in Vietnam.

It was their second meeting, after a historic one in Singapore last year.

They were meant to be talking about North Korea's nuclear weapons, and there was an expectation that they would announce some form of peace deal.

Most of the world wants North Korea to give up the powerful weapons - a process called denuclearisation. But North Korea believes if it didn't have nuclear weapons it could be attacked, so it won't give them up until it's convinced that's not going to happen.

What did they announce?

The leaders were all smiles when they went into their talks, but then it all ended much sooner than everyone was expecting. Mr Trump came out and said they hadn't managed to reach any deal at all.

At their last meeting back in June 2018, the two leaders signed a document promising the "complete denuclearisation" of the Korean peninsula, but there has been uncertainly around what exactly both sides mean by denuclearisation.

Mr Trump said North Korea had made a big offer - to dismantle the Yongbyon nuclear plant where it produces the material for nuclear bombs.

But in return they wanted all sanctions to be dropped, which Mr Trump said was not possible.

The US wants full nuclear disarmament before sanctions on the North can be lifted.

Trump told reporters: "Sometimes you have to walk and this was one of those times."

We haven't heard anything from North Korea yet.

What is likely to happen next?

It's not clear. So far there has also been no commitment between both leaders to hold a third summit, but White House press secretary Sarah Sanders said their respective teams "look forward to meeting in the future".

The US President said he was still "optimistic" and that the talks had left the two nations "in a position to have a really good outcome" in the future.

North Korea could, if it's really angry, start testing missiles and nuclear weapons again. That's a show of force and also helps it hone its military technology.

But the two men do appear to be good friends, so it might be they can try again.

It's a big personal defeat for Mr Trump, who had proudly told everyone that he was the man who could achieve a deal with Mr Kim.

Mr Kim hasn't really lost much and has got what he wanted - another meeting with the most powerful man on Earth.

For ordinary North Koreans, who live under incredibly tight government control and often don't have enough food to eat, nothing has really changed at all.

What does this mean for the relationship between North Korea and South Korea?

In April last year the leaders of North and South Korea met for the first time in 10 years, shaking hands at the border, and then holding hands as they crossed the military line between the two countries.

This was the first time a North Korean leader had set foot in the country of South Korea in 65 years, and showed a relaxing of tensions between the countries.

South Korean President Moon Jae-in has been on something of a personal mission to achieve a breakthrough with North Korea.

He has had his own landmark meetings with Kim Jong-un, but as Mr Moon can only serve one term in office, time could be running out for him to reach a deal with North Korea.

South Korea would have a lot to lose if North Korea decided to walk away from negotiations completely.

When Mr Trump was asked what he will say to South Korea's President Moon Jae-in following this summit, he said he'd be calling the leaders very soon.

"I like President Moon very much... we have a great relationship," said Mr Trump. "Believe it or not I have a great relationship with almost every leader but some take advantage of our country.

"We'll be calling Moon very soon and he'll be one of the first calls, I'll be calling Abe of Japan [too]. Moon is working very hard - he'd love to see a deal, he's been very helpful."