US President Donald Trump and North Korean leader Kim Jong-un have arrived in Singapore for their historic summit.

Mr Trump flew in aboard Air Force One, a few hours after Mr Kim touched down with his entourage.

Their meeting - the first between a leader from the North and a sitting US president - will take place on Tuesday on the resort island of Sentosa.

Mr Trump has described it as a "one-time shot" at peace and said the two were in "unknown territory".

The US hopes the summit will kick-start a process that eventually sees Mr Kim give up nuclear weapons. 

• The meeting that could change the world

The two leaders have had an extraordinary up-and-down relationship over the past 18 months, trading insults and threatening war before abruptly changing tack and moving towards a face-to-face meeting.

Mr Kim met Singapore's Prime Minister Lee Hsien Loong after he arrived. Mr Trump is also due to meet Prime Minister Lee before the summit begins.

Waiting for Kim

Rupert Wingfield-Hayes, BBC News, Singapore

For much of the day we've been playing "guess the plane". Three aircraft took off from Pyongyang, heading for Singapore.

The first was an Ilyushin transport plane. That was easy - it would be carrying Kim Jong-un's armoured limousine. Next came an Air China 747, which normally carries Chinese President Xi Jinping. Surely this would be carrying Mr Kim?

But then a surprise - Kim Jong-un's personal jet, a Soviet-era Ilyushin 62, also took to the air. Was he actually on that, or was it a decoy? It being North Korea, no-one was telling us. 

Singapore's foreign minister finally gave the game away, posting a photo of him greeting Kim on Instagram. It was, after all, the Air China 747.

It's been the same story with Mr Kim's hotel. That too is a secret. But then we spotted North Korean cameramen standing outside the St Regis Hotel. It was a pretty good clue. When Kim's motorcade arrived there was another little surprise - he wasn't in his normal Mercedes.

Instead he was riding an even fancier Maybach. It's not clear where it comes from. But it is clear that when it comes to planes and limos, Kim Jong-un has no intention of being outshone by President Trump.

How did we get here?

Mr Trump's first year in office was marked by bitter exchanges with Mr Kim as North Korea conducted several ballistic missile tests in defiance of international warnings.

The US president vowed to unleash "fire and fury" if Pyongyang kept threatening the US. He also referred to Mr Kim as "little rocket man".

In return, Mr Kim called him "mentally deranged" and a "dotard".

Despite the White House's "maximum pressure" campaign, the North remained defiant and carried out its sixth nuclear test in September 2017. Soon after, Mr Kim declared that his country had achieved its mission of becoming a nuclear state, with missiles that could reach the US.

But in early 2018, North Korea began attempts to improve relations with South Korea by sending a team and delegates to the Winter Olympics in Pyeongchang. 

In March, Mr Trump surprised the world by accepting an invitation from Mr Kim - delivered via Seoul - to meet in person. 

Since then, the path to the summit has been rocky, with Mr Trump at one point calling it off completely. But after some diplomatic scrambling, the two leaders will now sit down together.

Singapore is only the third country Mr Kim has visited since he became leader in 2011.

He made his first trip abroad as leader to China in March, and in April he became the first North Korean leader to step foot in South Korea when he met South Korean President Moon Jae-in at Panmunjom on their mutual border.

It is thought that Mr Kim went to boarding school in Switzerland. Recently, South Korea provided him with Swiss rösti at a summit meeting.

The US wants North Korea to get rid of its nuclear weapons in an irreversible manner that can be verified internationally. Only when steps begin to be taken in that direction will it "receive relief" from the grip of UN sanctions, Defence Secretary Jim Mattis recently said.

But this does not mean the US is expecting to get a final deal in Singapore. President Trump has described it as a "get-to-know-you situation" and said: "It's going to be a process."

Analysts say that Mr Kim, by winning the prestige of a meeting with the world's most powerful leader, has already gained a victory. They also question why he would give up his nuclear weapons after pushing so hard to get them.

Some say he would never do it, unless everyone else on the Korean peninsula disarmed too - including the US.

However, Mr Kim has also said he now wants to focus on building the North Korean economy - and thus wants sanctions relief and international investment.

The question is what concessions he is willing to make, and whether he will stick to any promises. Pledges to scrap the nuclear programme have been made before by his predecessors.

What could actually happen?

It's hard to say, but Mr Trump has signalled that they could sign an agreement to formally end the Korean War, which ended in a truce in 1953. Doing that, would probably be "the easy part", he said.

The US president has also said that if he thinks things are going badly, he will walk out of the meeting, but if things go well, Mr Kim could receive an invitation to the White House.

Secretary of State Mike Pompeo, who has met Mr Kim twice in recent months, said he believed he "is prepared to denuclearise" and agree "big and bold" changes.

But the North Koreans have not given much away about their position