The little girl vanished in 2007 from the apartment as her parents dined with friends at a tapas bar nearby.
Kate and Gerry McCann, of Rothley, Leicestershire, have previously spoken of their bitter regret about leaving Madeleine and her two-year-old brother and sister, twins Sean and Amelie, alone.
The investigation into Madeleine’s disappearance continues to this day, although it has been scaled down drastically.
Last month the Home Office confirmed £85,000 was being given to the UK-based Metropolitan Police inquiry to cover operational costs from April to September and, in all, more than £11 million has been spent on the inquiry so far.
A new programme from BBC’s Panorama, Madeleine McCann: 10 Years On, will be revisiting the story a decade on to reexamine the evidence and investigate what became of the men questioned by British police about the case.
What are the key theories about Madeleine McCann’s disappearance?
Burglary gone wrong
Madeleine may have woken up while an attempted robbery was taking place in the apartment.
She could then have been snatched when she disturbed the intruders.
In 2014 it emerged the Portuguese Attorney General had received a formal International Letter of Request from British officers investigating the mystery.
It was believed Met detectives made the request to interview three burglary suspects after mobile phone records placed them at the scene and revealed they had made an unusually high number of phone calls to each other shortly after the little girl disappeared.
They were arrested at the request of the Met and during interviews they admitted stealing from the apartments but denied they had anything to do with Madeleine’s disappearance.
Paulo Ribeiro was also questioned as part of this theory, and told the BBC’s Panorama: “I thought it was incredible.
“I knew of nothing when the police arrived at my door with a piece of paper that had a drawing on it, saying it bore a likeness to me and that someone had said I was involved and that I looked like the person who had kidnapped Maddie.
“I don’t know who that person was.”
Ribeiro claims to have been at home on the night in question and to never have been involved in any burglaries.
The BBC said Scotland Yard announced last week that there was no evidence to implicate the four men and the case against them had been closed.
In the days before she vanished, two other holiday flats in the same resort are reported to have been raided, with a child being awoken in one, though the suspects fled after the parents returned. The Portuguese police attached no significance to the incidents, however.
Ahead of the 10th anniversary of Madeleine’s disappearance, the Metropolitan Police admitted that this theory has still not been entirely ruled out.
Abducted by a paedophile
Madeleine may have been snatched by a sex offender who later killed her.
Nine sexual assaults and three “near misses” on British girls between 6-12 years old were identified on the Algarve coast by police in the three years before Madeleine’s disappearance, the Telegraph reports. In one of those cases, a 10-year-old was assaulted in an apartment in the resort of Praia da Luz.
Former Ocean Club waiter Euclides Monteiro was identified as a suspect in this attacks but he was already dead, having been killed in a tractor accident in 2009. He was eventually ruled out by DNA evidence, according to Sky.
There were also reports of a man seen carrying a child around Madeleine’s age on the night she disappeared and an e-fit was featured on BBC One’s Crimewatch.
The man remains a suspect.
Another image was also circulated after a friend of the McCanns, who was dining with them said she saw a man carrying a child in pink pyjamas when she went to check on her own child.
However, he was later identified by police and ruled out, according to the Telegraph.
Taken by child traffickers
This theory argues that Madeleine was taken by a gang of child traffickers, who took her abroad - probably to north Africa - and sold her into slavery.
It would not have taken long for a potential trafficker to drive to Portugal’s border with Spain from the resort. From there it would be easy to travel by boat to northern Africa.
Investigators have pursued leads in Morocco, which is on a trafficking route to Mauritania, which only abolished slavery in 1981.
This included numerous reported sighting of Madeleine, including a very similar-looking girl who was photographed in Tangier, later identified as local Bouchra Akchar.
The McCann family actually went to Morocco in the weeks following Madeleine’s disappearance to make an appeal for information.
Stolen to order for childless couple in pre-planned abduction
Madeleine could have been taken by a desperate couple who wanted a child of their own.
A number of people came forward to report people acting suspiciously around the resort at the time Madeleine vanished.
The son of a paedophile who lived an hour from the area at the time said that on his deathbed, his father claimed this was what had happened to the youngster.
Raymond Hewlett, whose past included a strong of child sex convictions and three jail terms, denied having anything to do with the disappearance of the toddler but said he knew she had been “stolen to order” by a gang who kidnap children for wealthy couples unable to have their own or adopt.
In 2013 the Met’s Detective Chief Inspector Andy Redwood told Crimewatch: “Madeleine McCann’s disappearance does, on one reading of the evidence, have the hallmarks of a pre-planned abduction.”
She wandered off
It has been posited that Madeleine could have woken up and gone looking for her parents.
The apartment in which the McCanns were staying had been left unlocked so if she had managed to get out of the door, she could then have wandered off into the night.
A number of things could have then happened to her, but theories include that she could have been hit by a car, fallen into a well or a roadworks pits near the resort or been abducted.
What now for the McCann family?
Kate and Gerry McCann have vowed to do “whatever it takes for as long as it takes” to find their daughter.
In an interview with the BBC’s Fiona Bruce, Madeleine’s mother said: “My hope for Madeleine being out there is no less than it was almost 10 years ago.”
Speaking ahead of the anniversary, the couple described it as a “horrible marker of time, stolen time”.
Last month, Scotland Yard said its officers are still pursuing “critical” leads to trace Madeleine, with officers receiving information on a daily basis.
Kate McCann said: “We just have to go with the process and follow it through - whatever it takes for as long as it takes. There is still hope that we can find Madeleine.”
Asked how the family would get through the anniversary, she added: “Every day is another day without Madeleine.
“I think we’ll get by as we have any other year really, we’ll be surrounded by family and friends, you know, obviously we’ll be there remembering Madeleine, as we always have.”
How will the 10th anniversary of Madeleine’s disappearance be marked?
A special service will be held on Wednesday for missing people in the Portuguese village where Madeleine disappeared 10 years ago.
The service, expected to last for about 30 minutes, will take place at the Church of Nossa Senhora da Luz at the time that Madeleine went missing, reports the Press Association.
A public gathering is also expected to take place in her home village in Rothley, Leicestershire.
In previous years, villagers have joined members of the McCann family near the local war memorial on May 3 to offer their support to the continued search for her.
Madeleine McCann: 10 Years On airs at 9pm on Wednesday 3 May on BBC One.