The subject of this review is to introduce a novel iterative methodology based on living anionic polymerization using specially designed 1,1-diphenylethylene (DPE) derivatives recently developed for the synthesis of well-defined many armed star-branched polymers with same or chemically different arm segments. The methodology basically involves only two sets of the following reaction conditions for the entire iterative synthetic sequence: (a) a linking reaction of a living anionic polymer with a DPE-chain-functionalized polymer, and (b) an in situ reaction of a DPE-functionalized agent with the anion generated by the linking reaction to reintroduce the DPE functionality usable for the next reaction. The number of arms to be linked by each stage of the iteration depends on the starting core and DPE-functionalized agents and can dramatically increase by the agent of choice. New functional asymmetric star-branched polymers involving conductive and rigid rod-like poly(acetylene) segment(s) have been synthesized by the methodology using the intermediate polymer anions produced by the linking reaction as macroinitiators to polymerize 4-methylphenyl vinyl sulfoxide, followed by thermal treatment of the resulting star-branched polymers. Star-branched polymers have been widely investigated because of the synthetic challenges associated with preparing them and because they offer unique physical properties quite different from the linear counterparts.1-14 Among star-branched polymers, asymmetric star-branched polymers having chemically different arms have recently attracted much attention because such star polymers should exhibit unique and interesting morphologies as well as properties due to their branched architectures and heterophase structures. As expected, they have exhibited quite different morphological maps from those of linear block copolymers and created novel periodical nano-objects with special shapes that promise potential applications in the field of nanotechnology. Although many star-branched polymers with well-defined structures have been so far synthesized, most of them are composed of less than five arms in regular star-branched polymer and less than three different arms in asymmetric starbranched polymer. The syntheses of regular star-branched polymers with many arms have been achieved only in a few cases even at the present time. With the most established methodology based on the linking reaction of living anionic polymers with multifunctional chlorosilane compounds, welldefined stars could be prepared with maximum arm numbers up to 18. 10,[36][37][38][39] It was also reported that advances in the synthesis of carbosilane dendrimers led to the successful synthesis of poly(1,3-butadiene) stars having 32, 64, and as high as 128 arms. 40,41 Validity of the chlorosilane linking agents throughout the synthesis of star-branched polymers with low molecular weight arms (M n $ 10 3 ) has recently been reevaluated by NMR and MALDI-TOF MS techniques.42,43 For stars having theoretically 32 and 64 arms, the average...