Hyperbranched polymers (HBPs) have attracted considerable attention during the past decade because of their intrinsic globular structures and unique properties, such as low viscosity, high solubility and a high degree of functionality, compared with linear analogs. As HBPs are generally prepared by one-pot polycondensation of an AB x monomer, where A and B represent two different functional groups, they are regarded as less-expensive alternatives to dendrimers. However, HBPs have randomly branched structures and their degree of branching (DB) is determined by statistics and only reaches B50%. Recently, several research groups have successfully synthesized a 100% DB without any defect mainly by condensation or addition reactions. These methods are based on a new concept in which the ratio of the rate constants, the first reaction rate constant (k 1 )/the second reaction rate constant (k 2 ) of an AB 2 monomer, can be controlled. Recent development in the synthesis of a linear polymer, that is, a 0% DB HBP, from an AB 2 monomer could make it possible to further precisely control the DB from 0 to 100% by using the same AB 2 monomer. In this review article, the backgrounds and methodologies for controlling the DB are described, especially focusing on recent advances in the synthesis of HBPs with a DB of 100, 0% and any percentage between 0 and 100%.