Image captionKim Wall boarded Peter Madsen's submarine Nautilus but we do not know what happened next
Swedish journalist Kim Wall, 30, disappeared during the night of 10 August.
She was last seen on the submarine of Danish inventor Peter Madsen, who has been charged with negligent manslaughter.
Police have for some time believed she was dead, and have said they think Mr Madsen deliberately sank his own sub before being rescued.
The inventor told police and closed-door court hearings that he threw her body into the sea after she died in an accident on board his submarine. Ten days after her disappearance was reported, a torso was found by a passing cyclist.
What do we know about Kim Wall's disappearance?
A highly respected freelance journalist, Ms Wall was researching a feature about Peter Madsen, an inventor who built his private 40-tonne submarine, UC3 Nautilus, through crowdfunding in 2008. She has written for the New York Times, Guardian, Vice and the South China Morning Post.
We know that they met at around 19:00 on Thursday 10 August at Refshaleoen, a harbour area in Copenhagen. She boarded the Nautilus as shown in the picture above and was reported missing by her boyfriend at 02:30 on Friday. The last picture of the pair in the sub's conning tower was taken at 20:30 by a man on a cruise ship, a short time before sunset.
The sub was not equipped with satellite tracking so after the alarm was raised in the early hours of Friday, rescue services searched for the vessel for hours.
It was not until 10:30 on 11 August that the first sighting was confirmed from a lighthouse in the Oresund.
However, a merchant ship has since reported coming within 30m of the unlit sub to the north-west of the Oresund bridge at about midnight on 10 August. Police say at that point the submarine crossed the channel from Denmark towards Sweden in the southern part of the Oresund.
What happened to Kim Wall?
What really happened to the Swedish journalist is either unknown or has been kept under wraps by Danish authorities.
Until 21 August, the closed-door nature of court hearings meant little information could be revealed. But after a request from both the defence and prosecution, we now know a little of what Peter Madsen has said.
According to his account, an accident occurred on board, Kim Wall died, and he "buried" her at sea somewhere in Koge Bay, about 50km (30 miles) south of Copenhagen. The nature of the alleged accident, and other details, remain undisclosed.
Hours after these details emerged, a woman's torso was found on the shore of Klydesoen, a short distance from Koge Bay. "When I say torso, it's a body without head, arms and legs," said Copenhagen police chief Jens Moller Jensen.
DNA tests are being conducted to find out if the remains belong to Ms Wall.
Mr Madsen's lawyer, Betina Hald Engmark, says her client has not confessed to anything and is still pleading not guilty. She says he gave evidence to the police during preliminary questioning and "information from this" has now emerged.
Has Peter Madsen's story changed?
Initially the inventor said he dropped Kim Wall off after dark at about 22:30 at the Halvandet restaurant, on the northern tip of Refshaleoen, close to where they had met earlier.
Restaurant owner Bo Petersen said the area was well covered by CCTV and he handed the video footage to police.
We do not know what was on the video but police said Peter Madsen gave them a new account of events. That account was not made public at the time.
Image captionPeter Madsen was eventually brought to shore late on Friday morning
Why did the submarine sink?
Within minutes of contact being established with Peter Madsen on the morning of 11 August, the submarine sank in Koge Bay. Copenhagen police said on 14 August that their forensic work on the sub confirmed "that the sinking of the submarine was allegedly a consequence of a deliberate act".
The inventor, well known in Denmark for his submarine and rocket activities, was soon brought ashore and interviewed by Danish reporters. The story was not yet a homicide inquiry.
What we still don't know
The big question remains what really happened to Kim Wall. Did she die in an accident? Or was she killed?
Danish and Swedish maritime authorities say they have determined the route the submarine travelled in Koge Bay and the Oresund strait before sinking.
Copenhagen police have urged people who have travelled with Peter Madsen before to explain what happened on their trips.
Image captionDanish police focused their investigation on the sub to dismantling its electronic equipment
Although the sub was brought to the surface, sea water is likely to have damaged any DNA evidence left on board. Police said they had secured "a substantial amount of electronics".
Why is the case behind closed doors?
This is not uncommon in Denmark.
It means that Peter Madsen's own lawyer is not allowed to give her client's story, other than to say he is innocent.
The charge of negligent manslaughter is seen as an initial step that will keep the defendant in custody until early September. It can later be changed or withdrawn.
Image captionThis is the last known picture of the sub taken before Kim Wall's disappearance
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This is possibly one of the darkest and most intriguing crime stories in recent years. Apparently this Madsen chap is a Elon Musk wannabe, he's built several submarines and was planning to build a rocket to go to space. Needless to say, his story doesn't add up one bit and the more information comes out the more disturbing it becomes.
