Trump and Kim are due to meet this spring. But if these talks fail could international arbitration provide - as it has in the past - an alternative way out of the North Korean crisis?
A year ago, productive north-south talks seemed inconceivable – but with the US tripping over its own feet, things are changing.
The admired US ambassador to Mexico is resigning, even as the two countries spat over trade, immigration and Trump's tweets. Can this critical diplomatic relationship survive yet another problem?
Legal technicalities and political priorities make it hard for North Koreans to settle on British soil.
The Trump administration shelved its plans for a 'bloody nose' attack while the Olympics in South Korea were under way. With the games over, it's time to consider the consequences of a strike.
North Korea clearly understands that going straight into high-level negotiations isn't always the way to make a breakthrough.
When he meets the US president this week, the prime minister will talk about the North Korean nuclear threat, the rise of China, and the rebranded Trans-Pacific Partnership.
Donald Trump doesn't have one foreign policy – he has several, and they all clash.
North Korea's cyber army is closely controlled by the ruling regime – a key difference from other countries' cyberattack and espionage groups.
Sometimes diplomacy won the day, sometimes it didn't.
The International Olympic Committee has banished dopers from the Winter Games. Shame it hasn't treated North Korea, a noted human rights violator, with the same resolve.
Parasites are not only a personal health problem – they are political too.
To avoid another refugee 'crisis' that would take the world by surprise, East Asia would do well to be prepared for an influx of people from North Korea.
Teams from both countries marched into opening ceremony under the unified Korea flag.
Kim Jong-un's favourite act won hearts and minds when they performed on day one of the Winter Olympics.
Korea's fielding of a unified Olympic team is an intriguing narrative of sport, international diplomacy and gender equality.
The mistrust between the two Koreas is so deep that there are more sceptics than enthusiasts over North Korea's involvement in the Winter Olympics.
In these Olympics more than most, there is less global attention on the medal count than on who will win the politics.
The joint South Korean-North Korean women's Olympic hockey team has angered fans of the game and raised concerns about athlete morale. But the media spotlight is actually good for the game.
North and South Korea explained in five questions and answers.