In recent years, along with growing concern about green chemistry, organocatalysis have been developed as novel catalytic systems due to its metal free nature. Because of their low toxicity and high chemical stability, organocatalysts have increasingly replaced metal catalyzed organic reactions. In particular, ring-opening polymerization (ROP) of cyclic esters, cyclic carbonates, and epoxides proceeded in a controlled/living fashion with organocatalysts. Previously, Hedrick and Waymouth mainly reported various basic or nucleophilic catalysts for ROP of lactide, lactones and trimethylene carbonate. In addition, we newly revealed organic super bases are suitable catalysts for ROP of epoxides. On the other hand, we and some other researchers investigated Brønsted acid catalysts to produce polyester or polycarbonate. In this review, we introduce our and their challenges for ROP using organocatalysts.