Recent efforts concerning nonbridged half-titanocenes containing anionic donor ligand of the type, Cp′TiX2(Y) [Cp′ = cyclopentadienyl group; X = halogen, alkyl; Y = anionic ancillary donor ligands such as aryloxo, ketimide etc.], as new types of olefin polymerisation catalysts have been reviewed. It has been demonstrated that these complexes displayed unique characteristics especially for ethylene copolymerisation affording new polymers by efficient incorporation of bulky olefins (so called “traditionally unreactive” monomers in transition metal catalysed coordination polymerisation), that have not been attained by the ordinary catalysts.