Answer by taking a quote from the following article:

Jarmusch was born January 22, 1953, in Cuyahoga Falls, Ohio, the middle of three children of middle-class suburbanites. His mother, of German and Irish descent, had been a reviewer of film and theatre for the Akron Beacon Journal before marrying his father, a businessman of Czech and German descent who worked for the B.F. Goodrich Company. She introduced Jarmusch to the world of cinema by leaving him at a local cinema to watch matinee double features such as Attack of the Crab Monsters and Creature From the Black Lagoon while she ran errands. The first adult film he recalls seeing was the 1958 cult classic Thunder Road, the violence and darkness of which left an impression on the seven-year-old Jarmusch.

Jarmusch's final year university project was completed in 1980 as Permanent Vacation, his first feature film. It had its premiere at the International Filmfestival Mannheim-Heidelberg (formerly known as Filmweek Mannheim) and won the Josef von Sternberg Award. It was made on a shoestring budget of around $12,000 in misdirected scholarship funds and shot by cinematographer Tom DiCillo on 16 mm film. The 75 minute quasi-autobiographical feature follows an adolescent drifter (Chris Parker) as he wanders around downtown Manhattan.  The film was not released theatrically, and did not attract the sort of adulation from critics that greeted his later work. The Washington Post staff writer Hal Hinson would disparagingly comment in an aside during a review of Jarmusch's Mystery Train (1989) that in the director's debut, "the only talent he demonstrated was for collecting egregiously untalented actors". The bleak and unrefined Permanent Vacation is nevertheless one of the director's most personal films, and established many of the hallmarks he would exhibit in his later work, including derelict urban settings, chance encounters, and a wry sensibility.  Jarmusch's first major film, Stranger Than Paradise, was produced on a budget of approximately $125,000 and released in 1984 to much critical acclaim. A deadpan comedy recounting a strange journey of three disillusioned youths from New York through Cleveland to Florida, the film broke many conventions of traditional Hollywood filmmaking. It was awarded the Camera d'Or at the 1984 Cannes Film Festival as well as the 1985 National Society of Film Critics Award for Best Film, and became a landmark work in modern independent film.  In 1986, Jarmusch wrote and directed Down by Law, starring musicians John Lurie and Tom Waits, and Italian comic actor Roberto Benigni (his introduction to American audiences) as three convicts who escape from a New Orleans jailhouse. Shot like the director's previous efforts in black and white, this constructivist neo-noir was Jarmusch's first collaboration with Dutch cinematographer Robby Muller, who had been known for his work with Wenders.  His next two films each experimented with parallel narratives: Mystery Train (1989) told three successive stories set on the same night in and around a small Memphis hotel, and Night on Earth (1991) involved five cab drivers and their passengers on rides in five different world cities, beginning at sundown in Los Angeles and ending at sunrise in Helsinki. Less bleak and somber than Jarmusch's earlier work, Mystery Train nevertheless retained the director's askance conception of America. He wrote Night on Earth in about a week, out of frustration at the collapse of the production of another film he had written and the desire to visit and collaborate with friends such as Benigni, Gena Rowlands, Winona Ryder and Isaach de Bankole.  As a result of his early work, Jarmusch became an influential representative of the trend of the American road movie. Not intended to appeal to mainstream filmgoers, these early Jarmusch films were embraced by art house audiences, gaining a small but dedicated American following and cult status in Europe and Japan. Each of the four films had its premiere at the New York Film Festival, while Mystery Train was in competition at the 1989 Cannes Film Festival. Jarmusch's distinctive aesthetic and auteur status fomented a critical backlash at the close of this early period, however; though reviewers praised the charm and adroitness of Mystery Train and Night On Earth, the director was increasingly charged with repetitiveness and risk-aversion.  A film appearance in 1989 as a used car dealer in the cult comedy Leningrad Cowboys Go America further solidified his interest and participation in the road movie genre. In 1991 Jarmusch appeared as himself in Episode One of John Lurie's cult television series Fishing With John.  In 1995, Jarmusch released Dead Man, a period film set in the 19th century American West starring Johnny Depp and Gary Farmer. Produced at a cost of almost $9 million with a high-profile cast including John Hurt, Gabriel Byrne and, in his final role, Robert Mitchum, the film marked a significant departure for the director from his previous features. Earnest in tone in comparison to its self-consciously hip and ironic predecessors, Dead Man was thematically expansive and of an often violent and progressively more surreal character. The film was shot in black and white by Robby Muller, and features a score composed and performed by Neil Young, for whom Jarmusch subsequently filmed the tour documentary Year of the Horse, released to tepid reviews in 1997.  Though ill-received by mainstream American reviewers, Dead Man found much favor internationally and among critics, many of whom lauded it as a visionary masterpiece. It has been hailed as one of the few films made by a Caucasian that presents an authentic Native American culture and character, and Jarmusch stands by it as such, though it has attracted both praise and castigation for its portrayal of the American West, violence, and especially Native Americans.  Following artistic success and critical acclaim in the American independent film community, he achieved mainstream recognition with his far-East philosophical crime film Ghost Dog: The Way of the Samurai, shot in Jersey City and starring Forest Whitaker as a young inner-city man who has found purpose for his life by unyieldingly conforming it to the Hagakure, an 18th-century philosophy text and training manual for samurai, becoming, as directed, a terrifyingly deadly hit-man for a local mob boss to whom he may owe a debt, and who then betrays him. The soundtrack was supplied by RZA of the Wu-Tang Clan, which blends into the director's "aesthetics of sampling". The film was unique among other things for the number of books important to and discussed by its characters, most of them listed bibliographically as part of the end credits. The film is also considered to be a homage to Le Samourai, a 1967 French New Wave film by auteur Jean-Pierre Melville, which starred renowned French actor Alain Delon in a strikingly similar role and narrative.

What did they do after this?
he achieved mainstream recognition with his far-East philosophical crime film Ghost Dog: The Way of the Samurai,