Greenberg gradually moved from intimate dramas toward more action-oriented fare, which suited him well when Hollywood came calling. Although he had worked on the routine US-produced Western, "Madron" (1970), which was shot in Israel, his first notable American film was Sam Fuller's expansive, hard-hitting and poetic war drama "The Big Red One" (1980). That same year he would also work with Boaz Davidson, an Israeli colleague from several past films, on "Seed of Innocence". Greenberg's Hollywood breakthrough, though, came with the exciting sci-fi actioner, "The Terminator" (1984), whose cinematography evoked both the dark, steamy violence of film noir and the coldly riveting grimness of high-tech fantasy. Greenberg and director James Cameron would team again for an excellent and more elaborate sequel, "Terminator 2: Judgment Day" (1991). Other work, meanwhile, has shown a flair for the slick imagery suited to modern screen horror, as with Kathryn Bigelow's striking "Near Dark" (1987) and the gentler fantasies of "Ghost" (1990).
Greenberg has also continued to work in drama ("La Bamba" 1987) and farce ("Three Men and a Baby" 1987). Indeed, his 90s work has suggested a move to milder fare, especially comedy, shooting the blockbusters "Sister Act" (1992) and "Dave" (1993). He returned to the action genre with "Eraser" (1996), Barry Levinson's sci-fi-themed "Sphere" (1997) and the Jackie Chan-Chris Tucker vehicle "Rush Hour" (1998).