A week since news broke that the half-brother of North Korean leader Kim Jong-un had been assassinated, a clearer picture is emerging of the Cold War-style killing in Kuala Lumpur's international airport.

But rumours still abound about the bizarre attack, and Malaysian police are keeping their cards close to their chest when it comes to their ongoing investigation.

Here is what we know - and what we still don't know - about the death of Kim Jong-nam.

What happened?

Last Monday morning, Kim Jong-nam was at the budget terminal of Kuala Lumpur's main airport preparing to fly to Macau.

He was approached by two women, one of whom grabbed him from behind and sprayed his face with an apparently poisonous liquid, according to police and leaked CCTV footage.

READ MORE: Half-brother of Kim Jong-un 'killed' in Malaysia

Jong-nam then approached airport staff, gesturing to his face in a bid to explain what happened, footage showed.

The staff later led him to the airport clinic, where a picture released in Malaysian media shows him slumped in a chair.

Kim suffered a seizure and was rushed to hospital but died before he arrived.

The first suspects

In the days following the attack, police announced they had arrested a 28-year-old Vietnamese woman called Doan Thi Huong, as well as 25-year-old Indonesian Siti Aishah and her Malaysian boyfriend.

Huong - who is shown in CCTV from the airport wearing a t-shirt emblazoned with the word "LOL" - worked at an "entertainment outlet" and Aishah was a masseuse at a spa, police said.

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Aishah had been duped into believing she was taking part in a TV prank show, the head of police in Indonesia said, citing information from Malaysia.

Residents of the rice farming village in Vietnam where Huong grew up said she was very fashionable, often changing her hair colour and returning each lunar new year with a different foreign boyfriend.

The Pyongyang trail

Later police arrested a 46-year-old North Korean called Ri Jong-chol, who they said lived in Kuala Lumpur and worked in information technology.

They are currently seeking four more North Korean men, who entered the country on different dates in the fortnight running up to the assassination, and all left on the day it was carried out.

The men returned to Pyongyang on a convoluted route via Indonesia, Dubai and Vladivostok, immigration officials and sources said.

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Seoul cited these developments as proof that the North Korean regime was behind the attack. But Pyongyang hit back, accusing the Malaysian investigation of being politically motivated.

The motive

If Pyongyang were behind the killing, a number of reasons have been put forward as to why the regime might have wanted Jong-nam out of the way.

One theory said he was a marked man since he criticised the country's system of hereditary succession to a journalist in 2011, when he said North Korea would need to reform and liberalise like China.

Another said Kim Jong-un was paranoid about the slim chance his older sibling posed a threat to his leadership, providing a liberal alternative within the Kim family.

Other analysts said the assassination could have been ordered over reports Kim Jong-nam was preparing to defect.

One suggestion that does not assume the regime's involvement is that a hit was ordered in connection with alleged shady business dealings in the region.

What happens next?

Malaysian authorities insisted a family member must come forward to provide a DNA sample before it can be released - something they said has yet to happen.

If no next of kin comes forward within a fortnight, police have said they would consider other options for the body.

A heavy, armed police presence accompanied the arrival of an unmarked convoy at the hospital holding the body in the early hours of Tuesday, amid unconfirmed reports that Kim Jong-nam's son, Kim Han-sol, had flown to Kuala Lumpur to claim the remains of his father.

A toxicology report should be released between one and two weeks after the post-mortem, the health minister has said on different occasions, which means there could be more detail about the kind of poison used as early as Wednesday.

But whatever the outcome of the investigation, the fallout from the killing has already damaged ties between North Korea and Malaysia and may isolate the Stalinist state yet further on the world stage.