Amorphous polymers exhibit a primary (glass, or alpha-) relaxation process and a low-temperature relaxation process associated with polymer backbone motion usually referred to as the beta-relaxation process. The latter process can be observed below the glass transition temperature of the polymer and usually merges with the alpha-relaxation process at temperatures somewhat above the glass transition temperature. While it is widely held that both the a-relaxation and beta-relaxation processes are engendered by localized (segmental) motions of the polymer backbone, and that there is a strong mechanistic connection between them, the molecular mechanisms of the alpha-relaxation and beta-relaxation processes in amorphous polymers are not well understood. Recently, atomistic molecular dynamics simulations of melts and blends of 1,4-polybutadiene have provided insight into the relationship between the alpha- and beta-relaxation processes in glass-forming polymers and an improved understanding of their molecular origins. (c) 2007 Wiley Periodicals, Inc.