Set in the 1950s, Voyager concerns the travels of an American construction engineer (Sam Shepard) who is wandering throughout Europe, recounting his life story through a series of flashbacks while meeting a variety of new characters. At first, he meets a man whom he knew during his time as a student in Europe in the days before World War II. Shortly afterward, he meets a beautiful young German woman (Julie Delpy), whom he accompanies on a journey to her home in Athens, Greece.