At precisely five minutes before high noon on March 6, 1970, the emergent radical-fringe bombers the Weather Underground had a terrifying and lethal showdown with its own cackhandedness.

In a townhouse on leafy, prosperous West 11th Street in Greenwich Village, close by houses once occupied by Poe, Melville and Whitman, there was, at 11.55am, a series of horrifying explosions; first one, then two more of equally shocking force. The detonations collapsed the three-storey house in on itself, leaving a ragged hole in the street's facade, as though a tooth had been torn from a smile.

A nearby neighbour - and our story is filled with odd connections like this - was one Susan Wager, who had briefly been the stepmother of sometime Weather-fan Jane Fonda. Emerging into the street, Wager was astonished to see two young women, one clad in jeans and soot, the other in just soot, staggering from the wreckage and narrowly escaping death a second time when the front of the building collapsed yards behind them. Offering them clothes, Wager then called the police, but returned to find the women had vanished.

They were Kathy Boudin, daughter of a progressive lawyer, and Cathy Wilkerson, daughter of the radio-station owner whose house had been destroyed. Unbeknownst to Wager, the pair were both on bail - Wilkerson for $20,000, Boudin for $40,000 - for destructive acts committed during the infamous Days of Rage protests fomented by a radical section of Students for a Democratic Society (SDS) in Chicago the previous autumn.

If the Days of Rage - which involved a minority of students tooling themselves up with bats and helmets and vandalising shopfronts along Chicago's Gold Coast - had seemed like anti-war politics at the very end of its tether - they were nothing compared to the campaign of bombings that the hardcore SDS splinter group that soon dubbed itself the Weathermen would commit during the early 1970s after announcing their decision to go underground to fight the power. Contradicting Bob Dylan, these young people believed that in fact you did need a weatherman to know which way the wind blew.

By then Dustin Hoffman, who lived in the house next door, was also outside examining the wreckage, a mild exemplar of the counterculture (since The Graduate), looking into the gaping maw left by members of the wilder peace movement. What police found inside the ruins was evidence of an accidental holocaust, arising from preparations for another, fully intentional one. Sixty sticks of dynamite were found, plus pipe bombs, a live anti-tank shell and stolen student ID cards from campuses across the country. One bomb-maker had inadvertently closed a circuit and immolated himself and two others. One corpse, identifiable only by the print on a severed finger, was that of Diana Oughton, daughter of an Illinois state politician, and granddaughter of the founder of the Boy Scouts of America. Ted Gold, a leader of the 1968 Columbia University shutdown, was also found in pieces, and of Terry Robbins there was only a torso remaining. It was understood later that the bombs were to have been detonated at a non-commissioned officers' dance at Fort Dix: apocalypse here and now, bringing the war home, indeed.

The end for the Weather Underground came 11 years later, with a botched armoured-car robbery in Nyack, upstate New York, that went even more horribly wrong. Still a fugitive, Boudin and her partner David Gilbert, another Columbia '68 veteran, had agreed to act as white getaway drivers for members of the Black Liberation Army (BLA), a formation composed of politicised street criminals and convicts radicalised in the aftermath of the 1970 Attica prison uprising. Although Gilbert and Boudin were unarmed, their cohorts killed three policemen, including the first black cop in the county. Another had his arm severed by machine-gun fire but survived, only to die in the World Trade Centre on September 11. Boudin pleaded guilty and received 25 years- to-life. Gilbert bought two life terms and will die in prison. In Attica, as it happens.

As documentarian Emile de Antonio asked in 1975: "What the hell is an essentially white, middle-class revolutionary group doing in America?" It's this question that fascinated film-makers Sam Green and Bill Siegel, whose remarkable documentary The Weather Underground now tells the whole story, or as much of it as can safely be related.

In the early 1970s, the group, operating in cells across the country, claimed up to 300 members, and planted over two dozen pipe bombs. They bombed the Pentagon, the US Capitol, NYPD HQ, the New York Board of Corrections (after Attica), and the offices of companies invested in Chile and Puerto Rico. The gruesome lesson of the Townhouse explosion ensured they always struck at night, in empty offices, and gave detailed advance bomb-warnings. They never killed anyone. They nevertheless expressed their solidarity with weird revolutionary groups like the Symbionese Liberation Organisation, which kidnapped Patty Hearst, and the BLA.

In 1976, they appeared on film, heavily disguised, for De Antonio and his cameraman Haskell Wexler. The resulting documentary, Underground, became a cause célèbre a year later when the FBI tried and failed to seize De Antonio's raw footage. By the end of the 1970s, most Weather people had surrendered themselves and, ironically, most were acquitted, or never charged, because the FBI itself had violated so many laws while hunting them down.

After three years of research, Green and Siegel persuaded several eminent Weathermen to speak, people once seen as fresh-faced young radicals in the SDS, and later glimpsed on the FBI's Ten Most Wanted list. Appearing in the movie are Bernadine Dohrn, la pasionara of the 60s student left, who - cue more surreal connections - had been a law school classmate of rightwing US attorney general John Ashcroft, Dohrn's husband Bill Ayers, whose memoir Fugitive Days - including his account of planting a bomb in the Pentagon - had the misfortune to be reviewed on page one of the New York Times on September 11 2001 (d'oh!), and David Gilbert, described by Green as "an absolute sweetheart, which is amazing since he's been locked up for 20 years".

Kathy Boudin declined to participate because she was facing a parole hearing - it was denied in 2002. Green and Siegel were also careful to include the dissenting opinions of SDS founder Todd Gitlin, who rightly says the Townhouse debacle proves that some Weathermen "were ready to be mass murderers", and of members of FBI Squad 47, who came to admire the Weather folks' ingenuity, but who used some fairly despicable methods in their hunt.

Then there is Mark Rudd, glimpsed as a beautiful young man yelling to a crowd of students, "We gotta knock these motherfuckers right on their asses!" and now a portly maths teacher at a community college in Albuquerque. Rudd says that when his students ask him what he did in the 1960s, he always announces, "I was a leading figure in a violent leftwing revolutionary organisation dedicated to the overthrow of the United States government." You can imagine those teenage jaws all dropping in unison. It's Rudd's way of making himself face the music, and of all the Weathermen, he seems the most conflicted and contrite. "I was drawn to the romance of the outlaw revolutionary." he told Newsweek recently, "But remember, we're talking about a 20-year-old kid. I'm not a violent person. I think I was posturing. I wanted to be tough."

The outlaw revolutionary: it was indeed a potent image. Weather activists often raved about Bonnie and Clyde as countercultural role models, and Gitlin recalls that Ayers and fellow SDS-er Jeff Jones comported themselves "like Butch and Sundance". Dohrn infamously congratulated the Manson Family in late 1969 for killing Leno and Rosemary LaBianca, saying: "Dig it! first they killed those pigs, then they ate dinner in the same room with them. Then they even shoved a fork into the victim's stomach. Wild!"

John Jacobs, another Columbia 1968 veteran: "We're against everything that's 'good and decent' in honky America. We will burn and loot and destroy." And as if to prove that, in the slogan of the time, " We're the people our parents warned us against," the Weathers abolished monogamy and embraced the acid-inflected orgy. One unpublished memoir quoted in the movie recounts a van ride into Chicago with a dozen revolutionaries fucking-for-chastity in the back.

To us today, and especially since September 11, these people and events have an almost Martian foreignness. Though the Weather Underground were the last in a long line of left-inclined bombers and violent insurrectionists - like John Brown the abolitionist, the Molly Maguires of the Pennsylvania coalfields in the 1870s, and the McNamara brothers, who killed 20 people when they dynamited the Los Angeles Times offices in 1910 - they still seem to defy comprehension. But as Sam Green says, "It's all about the context. Take away the context and what they did does seem insane, but given five years of the Vietnam war, years of nationwide protests and student anger, and it may simply have felt to them that all other rational avenues had been utterly exhausted."

Look at the events of the months before they disappeared. The Chicago police murdered the charismatic, highly effective Black Panther leaders Fred Hampton and Mark Clark in their beds; the My Lai massacre became public, the most gruesome images many Americans had ever seen; Nixon entered the White House and immediately escalated the war to insane levels; the Manson murders; Altamont - nothing but bummers and downers. "There seemed to be," says Brian Flanagan, "a mass mania in society." These were molten times, and something had to give.

The Weather people had no home but the struggle. They were inspirational figures in many ways, dedicated, visionary and effective activists in the mid-to-late-60s, but somehow got tangled up in sectarian infighting that isolated them from SDS and sent them finally underground. There they essentially deluded themselves on several fronts. Though they alone pointed up the centrality of race in American politics, they also developed a specious, patronising self-identification with developing-world revolutionary movements and domestic black groupings that they, as extremely privileged middle-class whites, had little in common with.

They also spurned the labour left, believing American workers had been "bought off" by consumer durables and bad TV. Rudd dissociated himself from the bombers early on and lived on the run, incognito within the working-class, people he suddenly realised he knew nothing about. Until then, he says in the movie, he'd been gripped "by this terrible, demented logic. I was seized by hate. I cherished it as a badge of moral superiority." After Saigon fell in April 1975, the Weather Underground was deprived of its primary raison d'être. All they were left with were sunglasses, wigs, safehouses, internecine struggles, criminal records and a debilitating sense of impotence. It was time to surface.

Twenty years later, they come across as intelligent, concerned citizens, justifiably proud of what they achieved before disappearing underground, less sure of their subterranean activities, but not altogether ashamed of them. There is something deeply reassuring about seeing ex-Weatherman Brian Flanagan, a working-class Irish-American, back behind the bar in the Manhattan saloon he owns, and something utterly surreal about seeing him on Jeopardy, the squarest TV game show ever, and winning $23,000 in the process. I'm guessing he didn't spend it on handguns or blasting caps, maybe just a few drinks on the house.

#183; The Weather Underground will be screened at the London film festival in the autumn.