Texas Governor John Connally adjusts his tie (foreground) as President and Mrs. Kennedy, in a pink outfit, settled in rear seats, prepared for motorcade into Dallas from the airport, Nov. 22, 1963.Corbis

Nearly 50 years after President John F. Kennedy was assassinated in Dallas, polls show many Americans still don't believe that assassin Lee Harvey Oswald was the only shooter or that he acted alone. These doubts have been fueled by inconsistencies in the official investigation by the Warren Commission in 1964, as well as dozens of investigations since then, including a House Select Committee of Congress that determined in 1979 that Oswald was not the lone gunman.

Criminal investigators say finding the means, motive and opportunity are the keys to solving a case, but it sometimes seems that the Kennedy killing consists of a swamp of shadowy characters, missing evidence and conclusions that lead nowhere. Here is a primer on the Kennedy conspiracy and why it continues to grab our attention today.

PHOTOS: JFK As You've Never Seen Him Before

Many eyewitnesses reported a fourth shot coming from somewhere in Dealey Plaza, the infamous "grassy knoll," shown here.Wikipedia Commons

The Warren Committee investigation found that Lee Harvey Oswald fired three shots at the president's motorcade as it traveled through Dealey Plaza on that fateful Friday afternoon of Nov. 22, 1963, and that all came from the sixth-floor of the Texas School Book Depository. Two shots struck the President, the second one killing him.

However many eyewitnesses reported a fourth shot coming from somewhere in Dealey Plaza, the infamous "grassy knoll." Using acoustic recordings, the House Select committee concluded that a second gunman fired at Kennedy. In 1982, a panel of experts from the National Academy of Sciences stated that the acoustics was flawed. Using bullet forensics, an investigation by the Reelz television network claimed this month that a Secret Service agent riding behind Kennedy accidentally shot him in the back of the head with an AR-15 assault rifle.

VIDEO: Forensics and the JFK Assassination

Lee Harvey Oswald with rifle and holding Marxist newspapers, taken in Oswald's back yard, Neely Street, Dallas Texas in March 1963. Wikipedia Commons

Oswald, a former Marine, had lived in the Soviet Union from 1959 to 1962, where he worked in a radio factory in Minsk. Some conspiracy theorists believe he had contacts with the KGB, the Soviet secret service, while either living in Russia or during his visit to the Russian embassy in Mexico City in September 1963.

Others say Oswald's irrational behavior were signs of someone with mental health issues, rather than connections with secret agents.

Lee Harvey Oswald and others handing out "Fair Play for Cuba" leaflets in New Orleans on Aug. 16, 1963Wikimedia Commons

Oswald went to Mexico City in September 1963 where he applied for a visa to visit Cuba. While living in New Orleans, he scuffled with anti-Castro groups while handing out pro-Castro leaflets on the street. Tensions between Cuba and the United States were high at the time. The assassination took place a year after the United States and Russia nearly came to war over nuclear weapons on the island.

Some authors have speculated that anti-Castro groups wanted Kennedy killed because of the failed Bay of Pigs invasion in 1961, or that Castro himself ordered the killing given the fact that the CIA had tried to kill Castro during Kennedy's time in office. But G. Robert Blakey, chief counsel of the 1979 House Select Committee, says that neither scenario was likely.

"We went down to Cuba, and we sat in Castro's office," Blakey, now a law professor at the University of Notre Dame, told Discovery News. "He was persuasive and said that he had nothing to gain. He said "I'm dealing with a capitalist system and I'm a socialist system; the people don't make a difference.' Why would he want to kill Kennedy to get Johnson?"

Lee Harvey Oswald's Coffin Goes Up For Sale

Jackie Kennedy leans over a dying President Kennedy as a Secret Service man climbs on back of car. Corbis

From the beginning, there have been suspicions that someone in the government either had a hand in the assassination or in covering up who did. After Kennedy died at Parkland Hospital, local medical officials wanted the autopsy done right away. However Secret Service agents scuffled with doctors at gunpoint and instead flew the body back to Bethesda Naval Hospital near Washington, D.C.

According to the House Select Committee, the CIA and the FBI blocked the earlier Warren Commission from both witnesses and other testimony about the assassination. The committee found that neither the FBI nor the Secret Service had adequately protected Kennedy before and during his trip to Dallas. Some theorists, such as filmmaker Oliver Stone, have speculated that "rogue agents" upset at Kennedy's politics directed Oswald to kill the president.

JFK Requested Bodyguards to Back Off

Carlos Marcello (C), his son Joe (L) and one of Carlos' attorneys leaves federal court Oct. 7, 1966 after Carlos testified before U.S. Commissioned Fritz Windhorst on charges that he slugged an FBI Agent at New Orleans Airport.Corbis

Kennedy came to office in 1960 promising a campaign against organized crime, and in November 1963, a number of mob figures were facing trial, including New Orleans mob boss Carlos Marcello.

In the 1980s, Marcello told cellmate Frank Van Laningham that he ordered Kennedy killed, not knowing that Van Laningham was an FBI informant at the time. Author Lamar Waldron writes in his new book "The Hidden History of the JFK Assassination" that Marcello imported two hit men from Europe who shot Kennedy from the grassy knoll. Waldron says the transcripts of the FBI jail tapes have still not been released.

"It's no surprise mobsters didn't talk," Waldron told Discovery News. "A dozen people can keep a pretty good secret if people's lives depend on it."