The name and the history of the club comes from the samizdat handwritten magazine CINE FANTOM issued by Igor Aleinikov since 1985. Olia Lialina, one of the original founers, was later a director. It was dedicated to history and theory of cinema. It had no officials analogs in the Soviet Union at this time. CINE FANTOM was associated with the Soviet cinema underground, Parallel Cinema (Parallelnoe Kino).
Cine Fantom Club programs have been screened at the Grenz Land Filmtage (Selb, 1995), the European Media Art Fest (Osnabruck, 1998), the Cottbus Film Festival (1995). In January 1999, works of the Cine Fantom Club were screened at the Anthology Film Archives in New York as part of an extensive program, Recent Russian Experimental Films.