It is more than 10 days since 30-year-old journalist Kim Wall disappeared after boarding Peter Madsen’s Nautilus submarine near Copenhagen.
Mr Madsen, an inventor, has been charged with manslaughter and police have confirmed that Ms Wall is presumed to have died.
A woman’s headless torso has been found close to where Ms Wall disappeared.
Copenhagen police chief Jens Moller Jensen told reporters: “When I say torso, it’s a body without head, arms and legs.”
Police do not know if the body is hers and precise details of the case remain sketchy.
Kim Wall, a Swedish reporter, was last seen on the evening of 10 August on board the 60ft Nautilus submarine that Peter Madsen had crowdfunded and built.
She had been interviewing him for an article.
What happened afterwards, however, is unclear.
Ms Wall was reported missing by her boyfriend in the early hours of Friday morning and authorities began a search for the missing submarine.
It resurfaced at around 10.30am, but sank soon afterwards and Mr Madsen was rescued by the Danish Navy as it went down.
He told authorities a technical problem had caused the boat to sink and that Ms Wall had been safely dropped off in Copenhagen the evening before.
However, she was still unaccounted for and when the submarine was searched police said it was found to have been sunk deliberately – although there was no body on board.
Mr Madsen was arrested the same day on suspicion of negligent manslaughter – but he denies any wrongdoing.
What new evidence has emerged?
On Monday 21 August police released information on Mr Madsen’s statement, revealing his story had changed.
He claimed Ms Wall had died in an accident on the submarine and that he dumped her body at sea.
The next day a cyclist discovered the torso at the edge of the water near Koge Bay.
Police said they were working to identify the body.
The investigation is being carried out behind closed doors and very little information has been given to the media.
Who are Kim Wall and Peter Madsen?
Peter Madsen crowdfunded and built the Nautilus submarine in 2008.
A description supplied by a TEDx event he spoke at described him as “an explorer, who excels in making fantastic dreams come true”.
Kim Wall was a respected freelance journalist who studied at Columbia University and the London School of Economics.
She wrote for publications such as the New York Times, Harpers and the Guardian, from countries including Cuba, Haiti and China.
Her stories included investigations into voodoo, furries and overseas investment in Uganda.
The International Women’s Foundation, which awarded a grant to Ms Wall, said it was “deeply saddened” at her disappearance.
“She was dogged in her pursuit of important and sometimes quirky stories,” their statement said. “She was adored by those who knew her.”
Ms Wall’s family said her work had brought her to many dangerous places, but that it was unimaginable that “something could happen… just a few miles from the childhood home.”