Negotiations between North Korea and the US have stalled after their second summit in early 2019 collapsed.
Here's an overview of a saga that has at times threatened nuclear war.
Why did North Korea develop nuclear weapons?
The Korean peninsula was divided after World War Two and the North developed an authoritarian form of government.
Isolated globally, it saw nuclear weapons as its only deterrent against a world it believed was seeking to destroy it.
Could it carry out a nuclear attack?
Probably. North Korea has carried out six nuclear tests.
It claims though this remains unverified, to have developed a nuclear bomb small enough to go on a long-range missile.
It also has a ballistic missile experts believe could reach the US.
How did talks begin?
After months of escalating mutual threats, in January 2018 Mr Kim said he was "open to dialogue".
Mr Trump accepted, ignoring past pre-talk conditions that North Korea denuclearise first.
On 12 June 2018, Mr Trump became the first sitting president to meet a North Korean leader.
The two signed an agreement committing to the "complete denuclearisation of the Korean peninsula" but with no detail on what that meant.
Back to stalemate?
Since then though, there has been little progress. The US wants North Korea to unilaterally give up its nuclear weapons while Pyongyang wants a step-by-step approach to ease the crippling sanctions regime.
On 28 February 2019, the two met for second summit in Hanoi but talks broke down over North Korea demanding sanctions relief.
Both sides say they remain open to future talks but there's no new summit scheduled.
Meanwhile, Kim Jong-un has also had meetings with Russian President Vladimir Putin and carried out new weapons tests widely seen as an attempt to increase pressure on the US.