The coordinator of a 1961 collage exhibit realized that much of the contemporary art he was seeing did not fit neatly into the standard categories: painting, sculpture, drawing, etc. Instead, what became known as Assemblage was and is composite art. Dubuffet had used the term since 1953.
Assemblage artists tend to use found objects, fragments and bits, often everyday manufactured materials or junk never intended as art materials.
So older pieces finally found acceptance in this new style, such as Joseph Cornell's 1940 piece, L'Egypte de Mlle Cléo de Mérode: cours élémentaire d'Histoire Naturelle -- a box containing bottles with various symbols of Egypt such as wheat and bits of text, all as might have been presented by the Khedive of Egypt to woo a celebrated 1890s French courtesan.
Louise Nevelson (1899-1988) from Kiev originally would scavenge materials from the streets of New York in the early morning hours, sculpt murals, and paint them uniformly. The results are often cityscape-like constructions that seem both to critique the junkiness of city living and to accentuate the distinctness of individual textures and components underneath the monochromatic overlay.
It is easy to find Assemblage hacks these days: crappy self-appointed artists who think they're accomplishing something profound but who are really just boring and slightly repulsing the rest of us. I am informed by one of my students that the film The Gleaners may offer some insight into the Assemblage impulse, although those who do not turn their collectings into artworks may need some special help.
The Art Book. London: Phaidon Press Ltd., 1996.
Dempsey, Amy. Art in the Modern Era: A Guide to Styles, Schools & Movements. NY: Harry N. Abrams Inc., Pub., 2002.