Recent examples for synthesis of group 4 transition metal (Ti, Zr, Hf) complexes, especially nonbridged half-metallocenes containing anionic donor ligands of the type, Cp′MX2(L) (Cp′=cyclopentadienyl group; M=Ti, Zr, Hf; X=halogen, alkyl etc.; L=anionic donor ligands), as catalysts for precise olefin polymerization have been reviewed. It has been revealed that these complex catalysts displayed unique characteristics especially for ethylene copolymerizations and some examples are known to produce new polyolefins that cannot be prepared by ordinary catalysts such as classical Ziegler–Natta, metallocenes. Modification of both cyclopentadienyl fragment and anionic ancillary donor ligands are the key for precise olefin (co)polymerization.