Hyperbranched polymers (HBPs), invented at the end of 1980s, are one important subclass of the fourth generation macromolecular architectures following the linear, branched, and crosslinking polymers. Due to their unique topological structure and interesting physical/chemical properties, HBPs have attracted wide attention from both academia and industry. HBPs are composed of linear units, dendritic units, and terminal units. The degree of branching (DB), a term to describe the composition of these three structure units and thus the branching architecture of polymers, is one of the most important intrinsic parameters for HBPs. This review has summarized the effect of the DB on the physical and chemical properties of HBPs, including the rheological property, crystallization and melting behaviors, glass transition, thermal and hydrolytic degradations, phase characteristics, lower critical solution temperature phase transition, optoelectronic properties, encapsulation capability, self-assembly behavior, biomedical applications, and so on. Such a structure and property relationship will build a bridge between the syntheses and applications of HBPs, especially in the application areas of functional materials, biomedical materials, and nanotechnology. (C) 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1277-1286, 2011