The mystery of what happened to famed American aviator Amelia Earhart — after she and her navigator disappeared in July 1937 during an attempt to circumnavigate the world — has captivated the public for generations.

Key points: The official account is that Earhart ran out of fuel en route to Howland Island

The official account is that Earhart ran out of fuel en route to Howland Island Others claim she died in Japanese captivity or secretly returned to the US

Others claim she died in Japanese captivity or secretly returned to the US A team working in PNG says she may have tried to turn around, crashing near Buka Island

But a team working in Papua New Guinea believes it may have cracked the case, and for the first time in more than 80 years, it at least has a plane wreck to investigate.

The Project Blue Angel team is probing the site of a crashed plane off the coast of Buka Island, in the country's Bougainville Autonomous Region, and recently completed a series of dives at the wreckage site.

Bill Snavely, the team's leader, believes Earhart and navigator Fred Noonan turned back towards Papua New Guinea when they discovered they were running low on fuel — the theory is currently being investigated by the team.

But it's still just one of several theories about what exactly happened to Earhart after she took off from the Papua New Guinean city of Lae, heading across the Pacific Ocean towards California.

Here's a look at five of the most popular Earhart stories that have done the rounds over the years.

1: Earhart crashed on the way to Howland Island

Earhart's flight to Howland Island was rough — there were strong headwinds, and poor radio communications. ( Library of Congress: Harris & Ewing )

The first major theory of what happened to Earhart — and the official position of the United States government — is that her Lockheed Electra 10E ran out of fuel, fell short of Howland Island, and now lies 5,500 metres below the surface of the ocean.

Chris Williamson is a man who knows a lot about Amelia Earhart: he first learned about her during a primary school history project, and pursued his interest in the aviator through university, where he wrote a dissertation on her.

He even moved to Earhart's birthplace of Atchison, Kansas and for more than 13 years he and wife Vanessa have run Chasing Earhart, a podcast and documentary series dedicated to her life and legacy.

"[After leaving Lae], they were 22,000 miles in with just over 7,000 miles to go to get to California," Mr Williamson told the ABC's Pacific Mornings program.

They planned to land at tiny Howland Island, about halfway between Hawaii and Australia, to refuel before reaching Hawaii and later California.

Map Zoom out on this map to get a sense of how tiny Howland Island is.

But the flight was rough — there were strong headwinds, and the radio communications were poor.

"As they near Howland, it's believed the Electra was down to her last 97 gallons of fuel, roughly — that's debated, but that's as close as we can get to official capacity [at that point in the trip]," Mr Williamson said.

A US coast guard ship waiting for the Electra off the coast of Howland Island was communicating with Earhart as she headed towards them, and its chief radio man later said he believed she was nearing the island, as signal strength readings for the Electra were growing stronger.

But the Electra never made it to Howland Island, and the ensuing 10-day search did not find any evidence of Earhart, Noonan or their plane.

2: The 'Japanese Capture' theory

This image, which has been debunked, was said to show Earhart sitting by a dock in the Marshall Islands. ( Reuters )

The lack of physical evidence following the search led to a proliferation of different theories, including the prominent Japanese Capture hypothesis.

This theory holds that Earhart made it to the island of Saipan in the Northern Mariana Islands, but that she and Noonan were then captured and later executed by the Japanese, who controlled the island at the time.

Other capture theories suggest she may have landed somewhere in the Marshall Islands, which were also controlled by Japan.

Several islanders have come forward in the past claiming to have seen Earhart and Noonan's execution, but evidence backing up their allegations has never emerged.

A photo even did the rounds a couple of years ago, purporting to show Noonan and Earhart on a dock on Mili Atoll in the Marshall Islands sometime in the 1930s.

This was later debunked after it emerged the photo, which was shot in Palau, was from a 1935 Japanese travel guide and therefore predated Earhart's final flight.

3: The Irene Bolam hypothesis

Some people assert Earhart (left) and Irene Bolam (right) were the same person, but Bolam always denied this claim. ( Wikimedia Commons )

The various Japanese capture claims spawned a popular spin-off that verged into conspiracy-theory territory.

The Irene Bolam hypothesis asserts Earhart was captured by the Japanese but not executed — instead, she was freed and repatriated to the United States under an alias.

"Some people believe that it was done in secret, with the help of [president Franklin D Roosevelt]," Mr Williamson said.

"She was declared dead in absentia in 1939, on January 5, and because of that she was, for all intents and purposes dead, Amelia Earhart assumed the identity of Irene Bolam.

"She lived out the rest of her days on the east coast on the United States, and she never flew again."

This theory made life difficult for the real Irene Bolam — a New York banker and plane enthusiast who, according to some, bore a strong physical resemblance to Earhart.

The hypothesis was first laid out in a book published in 1970, sparking a defamation lawsuit from Bolam, who said the authors appeared "more interested in fantasy than fact".

Bolam died in 1982 and always denied the allegations.

4: The castaway theory

Map A map showing the area where the bones were believed to have been found on Nikumaroro atoll.

There's also the castaway theory, which claims Earhart and Noonan landed on an island in Kiribati named Nikumaroro and lived out the rest of their lives there.

There was some conjecture that bones found in 1940 on the island may have belonged to Earhart, however, analysis done in Fiji the next year suggested they belonged to a man aged between 45 and 55 years old.

These bones are now lost, but measurements taken of the bones have become something of a battleground for investigators and researchers.

Last year, University of Tennessee anthropologist Richard Jantz published a study suggesting the measurements were consistent with photos of Earhart.

A 2015 study found the original assessment — that the bones belonged to a man — was still accurate. ( Wikimedia Commons )

He measured the length of her limbs based on the photos and compared them to the Nikumaroro bone measurements.

In 1998, Professor Jantz asserted the measurements were likely to have come from a woman of European ancestry, but a 2015 study by different researchers said the original assessment that the bones belonged to a male was correct.

5: The Buka Island wreck

Loading...

The Project Blue Angel researchers now investigating the wreck near Buka Island, led by Bill Snavely, suggest Earhart may have crashed after turning back towards Papua New Guinea due to fuel concerns.

Mr Williamson, whose wife, Vanessa, is working for Project Blue Angel, said it was the only team ever to have a plane wreck to work with.

"The aircraft happens to be in 100 feet [30 metres] of water, and it happens to share some consistencies with the plane that [Earhart] flew — granted there were a handful of planes that were very similar," he said.

"It's an aircraft and an aircraft site that has been screaming at people to investigate it for many years.

"[Bill Snavely] may be onto something, he may actually have cracked this thing."

But Mr Williamson also says that in a way, it doesn't matter if the mystery is ever solved.

"Maybe it doesn't matter how she died, maybe it only matters how she lived," he said.

"She was telling women: 'You can be engineers, you can be scientists, you can be aviators, you can be mathematicians … you can do what you want to do'."