Conçu comme un "documentaire fictif", la caméra suit les pas d'un jeune réalisateur tournant un film avec des musiciens de jazz et des artistes toxicomanes qui attendent chacun leur dealer d'héroïne : celui-ci se trouve être une même et unique personne, formant donc le lien (the connection) entre tous les protagonistes.
The musician Aurelius Rex and his wife Delia, a retired singer, are the recipients of an anniversary party in London thrown by a wealthy music promoter, Rod Hamilton.
The film follows a group of jazz musicians in the 1960s who play in small clubs and face constant financial hardships. Of the group, only one of them will go on to achieve success.
Adam Johnson is a talented African-American jazz cornetist, plagued by ill health, racism, alcoholism and a short temper, as well as guilt over the deaths years before of his wife and child. The result is a caustic personality that wears even on those who care the most about him, such as his best friend Nelson, and Vincent, a young Caucasian trumpeter whom Adam mentors. Arriving unexpectedly at his New York home drunk after walking out on his jazz quintet, Adam finds prominent Civil Rights worker Claudia Ferguson and her grandfather, Willie, who is himself a well-known jazz trumpeter, in his apartment. The two have been given access to the apartment by Nelson, but despite having authorized this, the drunken Adam is rude to both, that including making a vulgar pass at Claudia.
Sun Ra, who has been reported lost since his European tour in June 1969, lands on a new planet in outerspace with his crew "The Arkestra" and decides to settle African Americans on this planet. The medium of transportation he had chosen is music. He travels back in time and returns to the Chicago strip club where he used to play piano with the name "Sonny Ray" in 1943. There he confronts The Overseer (Ray Johnson), a pimp-overlord, and they agree on a duel at cards for the fate of the Black race. Each card drawn is a minor goal to achieve for Ra or The Overseer which will determine the winner of the duel. Then, to present time, Ra disembarks from his spaceship at Oakland and tries to spread his word by meeting with young Blacks at an Oakland youth centre and opening an "employment agency" to recruit people eager to move to the planet. He also agrees with Jimmy Fey (Christopher Brooks), the minion of The Overseer, to arrange radio interviews, a record album, and eventually a concert that will help him dictate his message. At the end, Ra takes Fey's "Black parts" with him to the spaceship, leaving him with his White parts. Fey, now acting white, leaves The Overseer who loses the duel. The planet Earth is destroyed after Ra's spaceship flies into space.
A group of Baker fans, ranging from ex-associates to ex-wives and children, talk about the man. Weber’s film traces the man’s career from the 1950s, playing with jazz greats like Charlie Parker, Gerry Mulligan, and Russ Freeman, to the 1980s, when his heroin addiction and domestic indifference kept him in Europe. By juxtaposing these two decades, Weber presents a sharp contrast between the younger, handsome Baker — the statuesque idol who resembled a mix of James Dean and Jack Kerouac — to what he became, “a seamy looking drugstore cowboy-cum-derelict,” as J. Hoberman put it in his Village Voice review.