The synthetic strategies available for the synthesis of miktoarm star (mu-star) polymers with molecular weight, chemical, or topological asymmetry are reviewed. All strategies are based on functional living polymer chains and linking agents. Although each strategy has its weak and strong points, it seems that anionic polymerization combined with chlorosilane methodology yields the widest variety of model single and double mu-stars. These novel architectures open new horizons in polymer science and technology.