Eight North Korean men, including a senior diplomat, have been identified as key suspects in the killing that was carried out at Malaysia's busiest airport by two women.
Who was Kim Jong-nam?
The 45-year-old was North Korean leader Kim Jong-Il's eldest son and the half-brother of Kim Jong-Un, who is currently at the helm.
He was once thought to be the natural successor to his father, the then-North Korean leader Kim Jong-Il.
But after Kim Jong-Il's death in 2011, his half-brother Kim Jong-Un, was chosen to lead North Korea.
Kim Jong-nam apparently fell out of favour with his father following a failed attempt in 2001 to enter Japan on a forged passport and visit Disneyland. After that, he lived in virtual exile, mainly in the Chinese territory of Macau. He also spent a lot of time in Japan.
Japanese journalist, Yoji Gomi, who wrote a book about him said he was "critical of the system that was in place in North Korea."
"He said that there he was able to enjoy singing and drinking alcohol with South Koreans, North Koreans and regular Japanese people, and he said he hoped that someday walls throughout the world would disappear like that."
Gomi also said that Kim Jong-nam told him he had never met his younger half-brother Kim Jong-Un who allegedly ordered his assassination.
How was Kim Jong-nam killed?
He was at the budget terminal of Malaysia's Kuala Lumpur 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.
Jong-nam suffered a seizure and was rushed to hospital but died before he arrived
Who were the women?
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.
North Korea's ambassador to Malaysia, Kang Chol, said police "should immediately release the innocent females from Vietnam and Indonesia."
What's the North Korean connection?
Malaysian police on Wednesday named two more suspects, a North Korean diplomat and a state airline official.
The diplomat wanted for questioning was 44-year-old Hyon Kwang Song, a second secretary at the embassy. Police also want to interview Kim Uk Il, 37, an employee of the North Korean state-owned airline Air Koryo.
Another suspect identified as Ri Jong Chol, has been in custody since last week, and said Ri Ji U, remains at large. Malaysia's police chief, Khalid Abu Bakar, said police "strongly believed" four others were back in the North Korean capital of Pyongyang, having fled Malaysia on the day of the attack.
The police chief said he believed the North Korean men were "heavily involved" in the murder.
What's the official response?
"It has been seven days since the incident, but there is no clear evidence on the cause of death and at the moment we cannot trust the investigation by the Malaysian police," North Korea's ambassador to Malaysia, Kang Chol, said.
Malaysian Prime Minister Najib Razak backed those running the investigation, saying it was "very professional."
On Monday, Malaysia recalled its envoy to North Korea.
The diplomatic row erupted after North Korea insisted Kim Jong-nam's body be returned and objected to an autopsy.
Malaysia rejected the request, saying the remains must stay in the morgue until a family member identifies them and submits a DNA sample.
No next-of-kin have come forward, the police chief said.
What's the latest in the murder case?
Malaysian police on Wednesday said the two women arrested in connection with Kim Jong-nam's death knew what they were doing.
"I think you have seen the video, right? The lady was moving away with her hands towards the bathroom. She was very aware that it was toxic and that she needed to wash her hands."
The second secretary at the North Korean embassy in Malaysia, Hyon Kwang Song, is also wanted for questioning by police.