Despite two summits and one historic meeting at the Korean border, the future of the US-North Korea talks is uncertain.

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 a deterrent against a world it believed was seeking to destroy it.

Could it carry out a nuclear attack?

Probably. Pyongyang has carried out six nuclear tests.

It claims, though this remains unverified, to have developed a nuclear bomb small enough for a long-range missile.

It also has a ballistic missile experts believe could reach the US, and in 2018 appeared to develop a submarine-capable missile.

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, 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 a second summit in Hanoi but talks broke down over North Korea demanding sanctions relief.

Meanwhile, North Korea carried out new weapons tests widely seen as an attempt to increase pressure on the US.

On 30 June, the leaders met again at the border between the two Koreas and Donald Trump briefly stepped into the North.

Yet as US-South Korea military drills loomed in July and August, Pyongyang ramped up its missile tests as a “warning”.

Another round of talks in October failed to make any new progress.

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