Beginning in 1972, Hassell studied classical Indian music under the tutelage of Pandit Pran Nath, modifying Nath's vocal techniques to the trumpet to develop the Fourth World concept, which he introduced with 1978's Vernal Equinox. The jazz-inspired Earthquake Island appeared a year later, and in 1980 Hassell issued Possible Musics/Fourth World Vol. 1, a collaboration with Brian Eno. (A sequel, Dream Theory in Malaya/Fourth World Vol. 2, was quick in forthcoming.) Through Eno, he also began working with a series of experimental pop acts, appearing on records by Talking Heads, David Sylvian and Peter Gabriel; in 1982, Hassell additionally scored Magazzini Criminali's Venice production of Sulla Strada, earning an Ubu award for Best Music for a Theatrical Work.
Following 1983's Aka-Dabari-Java/Magic Realism (co-produced by Daniel Lanois), Hassell did not resurface on record until 1986's Power Spot; in the interim, he composed Pano de Costa, a string quartet piece recorded by the Kronos Quartet for their White Man Sleeps LP. The Surgeon of the Nightsky Restores Dead Things by the Power of Sound followed in 1987, and that same year Hassell collaborated with the Burkina Faso percussion ensemble Farafina, a union which spawned 1989's Flash of the Spirit. The hip hop-inspired City: Works of Fiction appeared in 1990, and four years later he launched Dressing for Pleasure; subsequent projects include Lurch, an experimental dance piece choreographed by Gideon Obarzanek, and 1999's Fascinoma, on which Hassell collaborated with Ry Cooder and Jacky Terrasson. Hollow Bamboo was issued a year later.