Methods of making polyisobutylene and catalyst systems are described. Polyisobutylene compositions and catalyst system compositions are also described. In some embodiments, a method of making a catalyst system includes: providing a support material; calcining the support material; and forming a catalyst system by adding to the support material (a) a mixture comprising BF3, (b) a mixture comprising BF3 and a complexing agent, or (c) both. In some embodiments, a method of making a polymer composition includes providing a catalyst system comprising: (a) a support material selected from the group consisting of Al2O3, ZrO2, TiO2, SnO2, CeO2, SiO2, SiO2/Al2O3, and combinations thereof; and (b) BF3; providing a feedstock comprising isobutylene; forming a reaction mixture comprising the feedstock and the catalyst system; contacting the isobutylene with the catalyst system; and obtaining a polymer composition.