This invention relates to the field of olefin polymerization catalyst compositions, and methods for the polymerization and copolymerization of olefins, including polymerization methods using a supported catalyst composition. One aspect of this invention is the prepraration and use of a catalyst composition comprising a hydrocarbyl-substituted metallocene compound and a chemically-treated solid oxide for olefin polymerization processes. In another aspect, for example, this invention encompasses the preparation of a catalyst composition comprising (.eta.5-cycloalkadienyl).sub.2Zr(hydrocarbyl).sub.2 complexes and sulfated alumina, but containing no organoaluminum or organoboron cocataysts, and further the use of this catalyst composition for polymerizing olefins.