There is never an ordinary day at Dallas’ Dealey Plaza, where personal revelations and quiet mourning are as familiar as the downtown rush-hour traffic. But this August afternoon is stranger than usual: A dark blue 1961 Lincoln Continental convertible limousine is sitting in the center lane of Elm Street, which has been blocked off. Stills of the Zapruder film line the sidewalk, serving as the storyboard for the day’s activities: a restaging of the century’s most famous murder, the assassination of John F. Kennedy, for a television documentary that will try to determine, with the help of lasers, where the shots came from. Three men in white shirts are huddled around the convertible, bending and shifting the limbs of its foam rubber passengers. A gray dummy sits in the back seat, just as Kennedy did, while another—in John Connally’s place—rests on the jump seat in front of him. “His arm has got to come over more,” insists one man, pulling the president’s left arm farther across his spongy torso. A film crew circles the scene, while tourists, ballistics experts, conspiracy buffs, and reporters watch the goings-on. “But shouldn’t his other hand be over the chrome line?” asks one observer. The men in the white shirts mull this over, glancing first at the film stills and then at the mannequins, before resuming their work. The heat is oppressive, but the comparing and tweaking continues late into the day.

Of course, they will never get it right: the precise slant of a wave, the tilt of a head, the trajectory of a bullet. Elm Street has been closed several times for such reenactments, but there is still no consensus on exactly what happened. There are too many shifting perspectives, inexplicable details, and active imaginations, all aching to make sense of a senseless act. Over the past 35 years, countless theories have evolved, but they discount the overwhelming proof, both physical and circumstantial, that Lee Harvey Oswald was the man who shot Kennedy. “I have sent men to the electric chair with less evidence,” said Henry Wade, Dallas County’s district attorney in 1963.

In 1964 the Warren Commission concluded that Oswald was Kennedy’s assassin, and that he had acted alone. But the official story had troubling inconsistencies: Conflicting eyewitness accounts, discrepancies in the autopsy reports, and the unlikely paths and precision of Oswald’s shots all suggested more than one gunman had been at Dealey Plaza. The first cries of foul play came from across the Atlantic, most notably from English writer Bertrand Russell, but it wasn’t until 1966, with the publication of Mark Lane’s Rush to Judgment and Edward Jay Epstein’s Inquest, that the Warren Commission’s findings were challenged at home. Life magazine, which had purchased the Zapruder film soon after the assassination, launched a new investigation of the case. The magazine’s consultant, former Navy lieutenant Josiah Thompson, argued the following year in Six Seconds in Dallas that a close examination of the film showed the president being shot from several directions, hence a conspiracy.

New Orleans district attorney Jim Garrison stepped into the fray in 1967, using the loose ends of Oswald’s life—he had defected to the Soviet Union and sought asylum in Cuba and had tenuous connections to anti-Castro militants—to speculate that the CIA had somehow been involved. For the most part, the public ignored such cynical talk, but as first Vietnam and then Watergate wore on, its distrust grew. Interest in a more thorough investigation of the Kennedy assassination reached critical mass in 1975, when the Zapruder film was first shown on TV and Senate hearings revealed that the CIA had conspired with the Mafia to kill Fidel Castro in the early sixties. The following year, the House Select Committee on Assassinations (HSCA) was formed, and in 1979 it concluded that while Oswald was indeed the gunman, he had had an accomplice, who shot, and missed, from the grassy knoll. The existence of a conspiracy was confirmed—by the federal government, no less. The HSCA also hinted at involvement by Cuban exiles or members of the mob, a theory that remained in vogue throughout the eighties. Since 1991, when Oliver Stone’s controversial movie JFK used Garrison as its hero and pointed fingers at the CIA, the FBI, Cuban exiles, military intelligence, and munitions profiteers, the specifics of the various theories have been lost, replaced by a sense of overall complicity: Everyone was in on it.

What follows is an overview of the conspiracy oeuvre, though it is hardly exhaustive. We haven’t included some of the shadowy figures—Umbrella Man, the Babushka Lady, Badge Man—that populate the fringes of conspiracy-think. Nor do we examine the more far-out theories: that Joe DiMaggio, angered at Kennedy’s treatment of his ex-wife, Marilyn Monroe, got his Italian friends to knock him off; or that the president, who was already suffering from Addison’s disease, staged his own death, ensuring a glorified place in history; or that Frank Sinatra’s drummer, Franklin Folley, was somehow involved. Instead, we present the ones that have endured over the years. They are as intriguing as they are implausible, and they raise as many questions as the Warren Commission failed to answer. Underlying all of them are uncanny coincidences, convergences of terrible knowledge, and most important, a desire to believe that there was a grand design—some kind of meaning and purpose—behind Kennedy’s murder. Thirty-five years later, these narratives have become more appealing than the banal alternative: a lone nut, a good shot, an utterly vain death.