Madeleine McCann vanished while on a family holiday in Praia da Luz in the Algarve, Portugal, in May 2007.
The three-year-old went missing from the family's apartment, while her parents Kate and Gerry were having dinner with a group of friends just 100 yards away.
Recently, 15 years after her disappearance, the Portuguese police named German sex offender, Christian B as a person of interest in the case.
Over the years several new theories have come up on what might have happened to the toddler. Here are seven of the most famous theories.
Burglary gone wrong
One theory is that Madeleine woke up during a burglary, suggesting someone who had entered the apartment panicked and attacked her, and that he decided to carry her off.
In 2014, Scotland Yard is thought to have questioned four local suspects in Portugal on this theory. They were later ruled out, and Portuguese police dismissed the theory.
One reason that experts don't believe this theory is that such a spontaneous act.
Carrying a toddler away when it wasn't in the plan would likely lead to mistakes or leave some trail of evidence.
Snatched by a local paedophile
Madeleine McCann's parents hope she is alive as German paedo named official suspect
A second theory suggests that young Madeleine was the victim of a paedophile who snatched her and later killed her.
There are some alleged witnesses to support the presence of several suspicious men watching the McCanns' apartment in the days before and on the day of Maddie's disappearance.
This theory was pursued by Portuguese detectives when the case was reopened for investigation in 2011 by studying a series of attacks that took place long the Algarve coast in the years up to 2007.
Madeleine McCann suspect Christian B 'makes explosive TV claim he has alibi'
In all these cases, a man had entered the apartments and villas of mainly British holidaymakers and molested young girls while they slept.
Portuguese investigators believed it was all done by the same man – former Ocean Club waiter Euclides Monteiro being their suspect.
However, Monteiro was killed in a freak tractor accident in 2009, and he was eventually also ruled out in the Madeleine case by DNA evidence.
Abducted by a childless couple
Another theory suggests that Madeleine was kidnapped by a couple who couldn't have a child of their own or had lost their child.
This theory would suggest that Madeleine could be alive and being cared for.
However, the hole is this theory is that such a kidnapper is more likely to have abducted a younger child, like Madeleine's twin siblings Sean and Amelie, who were sleeping beside her and were only two years old, who may have been less likely to resist or wake up.
Taken by child traffickers
A more sinister abduction theory suggests that Madeleine was kidnapped by a gang, taken abroad and sold into slavery.
This was an early theory that was explored by Portuguese investigators after a report that Madeleine had been photographed on the beach by a stranger.
Several witnesses have also claimed to see Madeleine in Morocco, a country on the trafficking route to Mauritania.
Given that human trafficking gangs often operate in the northwest African country of Mauritania, this theory is one of the more logical ones for Madeleine's sudden disappearance.
Another theory is that Madeleine woke up and went looking for her parents. The theory assumes that the toddler may have been able to open the patio door and garden gate to walk out.
The theory suggests that she walked down the hill and fell into a roadworks pit and died there, that she was hit and killed by car or that she climbed into a small space which she couldn't get herself out of.
Sinister occult forces took her
While there are plenty of logical theories around Madeleine's disappearance, there are also more imaginative conspiracy theories that link the toddler's disappearance to everything from the Illuminati to so-called Pizzagate.
Pizzagate is a debunked conspiracy theory, which claimed that Hillary Clinton and her former campaign chair, John Podesta, ran a child sex ring at the basement of a pizzeria in Washington DC.
Among those wrongly demonised by Pizzagate were John and Tony Podesta, who were later accused of being the McCann kidnappers when a resemblance was noted between the Podestas and some e-sketches related to Madeleine's case.
Thought the sketches are actually of a single suspect, this hasn't dampened conspiracies around Podestas or other VIP traffickers being behind Madeleine's disappearance.
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