The initiation and catalysis of isobutylene polymerization from several new metallocene and nonmetallocene initiator-catalysts that contain the noncoordinating anions (NCA), B(C6F5)(4)(-) and RB(C6F5)(3)(-) is reported. Application of these initiator-catalysts is extended to styrenics and vinyl ethers. The NCA does not contribute to termination and can be used in low concentrations compared with conventional Lewis acids. These qualities provide for isobutylene polymerizations that yield low M(n) oligomers or high M(n) polymer, dependent upon the initiator and polymerization conditions. Mechanistic aspects of initiation, transfer and termination as well as the participation of adventitious water are considered for each class of initiator-catalyst. The influence of the NCA on the stereoregularity of cationic styrene polymerization is also considered. NCAs do not cause the stereospecific carbocationic polymerization of styrene. We suggest that under conditions not conducive to carbocationic polymerization, NCA/metallocenes mediate the coordination polymerization of styrene.