The synthesis of miktoarm star (mu-star) polymers by the methodologies based on living anionic polymerization is reviewed, with a particular focus on precisely controlled architectures of the synthesized mu-star polymers, such as molecular weight, molecular weight distribution, arm number, and composition. Among these methodologies, a novel and versatile stepwise "iterative methodology" recently developed by us is mainly introduced in this article. The iterative methodology is designed in a way that the same reaction site is regenerated after the arm introduction in each reaction sequence and this sequence is repeatable. The development of this methodology allows successive and, in principle, limitless introduction of arm segment into mu-star polymers. Consequently, a variety of new and synthetically very difficult multi-armed and multi-component mu-star polymers with well-defined architectures have been synthesized. They were composed of polyisoprene, poly(styrene)s, poly(2-vinylpyridine), poly(methyl methacrylate), various methacrylate-based polymers, and even poly(acetylene) as arm segments. (C) 2013 The Authors. Published by Elsevier Ltd. All rights reserved.