Hoffa, then 62, was last seen on July 30, 1975, at suburban Detroit restaurant. He was there ostensibly to meet with reputed Detroit Mafia street enforcer Giacalone and Anthony Provenzano, chief of a Teamsters local in New Jersey, who was later convicted in a murder case. Both men have since died.
Hoffa believed Giacalone had set up the meeting to help settle a feud between Hoffa and Provenzano, but Hoffa was the only one who showed up for the meeting, according to the FBI.
Giacalone and Provenzano later told the FBI that no meeting had been scheduled.
The FBI said at the time that the disappearance could have been linked to Hoffa's efforts to regain power in the Teamsters and to the mob's influence over the union's pension funds.
Police and the FBI have searched for Hoffa intermittently ever since.
In September 2001, the FBI found DNA that linked Hoffa to a car that agents suspected was used in his disappearance.
In 2004, authorities removed floorboards from a Detroit home to look for traces of blood, as former Teamsters official Frank Sheeran claimed in a biography that he had shot Hoffa. Sheeran had died in 2003.
Investigators ruled that blood found in the house was not Hoffa's. The FBI has a sample of his DNA from a hairbrush.
Two years later, the FBI razed a horse barn in Michigan following what it called "a fairly credible lead."
But the disappearance remains unsolved.
Urban lore long suggested that Hoffa was buried around the end zone at the former Giants Stadium in New Jersey.
As TruTV puts it, the mystery surrounding Hoffa is not simply a "whodunnit."
"The likely suspects are all known, and their motives are well documented. The question is: Where? What exactly did they do to Jimmy Hoffa, and where did they dispose of his body?"
But over the years, numerous theories have been floated. In 1987, Joe Franco -- a former Hoffa strong-arm -- and a New York Times reporter published "Hoffa's Man," which Fortune described as "the hair-raising inside story of Jimmy Hoffa."
"Rather than being kidnapped by rival union forces as law enforcement authorities have long speculated, Franco says Hoffa was abducted by two federal agents," Fortune reported. "He thinks they drove Hoffa to a nearby airport, took off in a small plane, and pushed him out over one of the Great Lakes. Franco says he did not tell federal investigators this bizarre, and unverifiable, story because they would not grant him immunity."
Hoffa's son, James P. Hoffa, is the current president of the Teamsters.
CNN's Chuck Johnston and Stephanie Gallman contributed to this report.
