Some recent successful examples for synthesis of new polyolefins by coordination insertion polymerization using nonbridged half-titanocenes containing anionic donor ligands of the type, Cp’TiX₂(L) (Cp’ = cyclopentadienyl group; X = halogen, alkyl etc.; L = anionic donor ligand) have been reviewed.  These complex catalysts display unique characteristics especially for ethylene copolymerizations and synthesis of new polyolefins that cannot be prepared by ordinary catalysts such as classical Ziegler-Natta, metallocenes. Modification of both cyclopentadienyl fragments and anionic ancillary donor ligands are the key for precise olefin (co)polymerization.