This article summarizes recent examples for precise synthesis of (co)polymers containing functional end groups prepared by living ring-opening metathesis polymerization (ROMP) using molybdenum, ruthenium complex catalysts. In particular, this article reviews recent examples for synthesis of amphiphilic block/graft copolymers by adopting transition metal-catalyzed living ROMP technique. Unique characteristics of the living ROMP initiated by the molybdenum alkylidene complexes (so-called Schrock type catalyst), which accomplish precise control of the block segment (hydrophilic and hydrophobic) as well as exclusive introduction of functionalities at the polymer chain end, enable us to provide the synthesis of block copolymers varying different backbones by adopting the “grafting to” or the “grafting from” approach as well as “soluble” star shape polymers with controlled manner. The “grafting through” approach (polymerization of macromonomers) by the repetitive ROMP technique offers precise control of the amphiphilic block segments.