The polymerization of isobutylene allows us to obtain a wide spectrum of polyisobutylenes (PIBs) which differ in their molecular weight characteristics and the chemical structure of chain-end groups. The bulk of the PIBs manufactured worldwide are highly reactive polyisobutylenes (HRPIBs) with -C(Me)=CH2 end-groups and low-molecular weights (Mn < 5 kDa). HRPIBs are feedstocks that are in high demand in the manufacturing of additives for fuels and oils, adhesives, detergents, and other fine chemicals. In addition, HRPIBs and CMe2Cl-terminated PIBs are intensively studied with the aim of finding biomedical applications and for the purpose of developing new materials. Both chain control (molecular weight and dispersity) and chemoselectivity (formation of exo-olefinic or -CMe2Cl groups) should be achieved during polymerization. This review highlights the fundamental issues in the mechanisms of isobutylene polymerization and PIB analysis, examines actual catalytic approaches to PIBs, and describes recent studies on the functionalization and applications of HRPIBs and halogen-terminated PIBs.