While many of the theories are bizarre, one longstanding view is the towers would not have collapsed in the way they did if they were hit by aircraft.
Some claim there must have been a "controlled detonation" at ground level for the Twin Towers to fall in on themselves as they did.
One key part of their argument is the collapse of a third smaller tower, called Building 7, at the World Trade Centre complex, several hours after the huge skyscrapers fell.
Until now, the theory has been just that and confined to the online forums of conspiracy theory websites.
But now, the University of Alaska is sponsoring a full investigation into claims that World Trade Center Building 7 was brought down by a controlled demolition during the 9/11 attacks.
The official version of events is that fire spread to Building 7, from the main towers, devastating the structure, and causing it also to fall in on itself.
Footage of the tower consumed by fire emerged in 2011, and it was thought the conspiracy may have been killed off.
But Dr J Leroy Husley, chair of the University of Alaska Fairbanks’ (UAF) Civil and Environmental Engineering Department, has partnered with architects and engineers linked to campaign group 9/11 Truth to evaluate the causes of its collapse.
A report on Activistpost.com said: "Although questions still remain about how the two planes that hit the Twin Towers could cause the total collapse of the high-rise buildings, many 9/11 researchers now focus on the mysterious collapse of Building 7.
"A number of 9/11 family members point to the collapse of WTC7 as a possible crack in the official story that could spark a new national conversation on the events of that day.