The present invention generally relates to alcohol-terminated polyisobutylene (PIB) compounds, and to a process for making such compounds. In one embodiment, the present invention relates to primary alcohol-terminated polyisobutylene compounds, and to a process for making such compounds. In still another embodiment, the present invention relates to polyisobutylene compounds that can be used to synthesize polyurethanes, to polyurethane compounds made via the use of such polyisobutylene compounds, and to processes for making such compounds. In yet another embodiment, the present invention relates to primary alcohol-terminated polyisobutylene compounds having two or more primary alcohol termini and to a process for making such compounds. In yet another embodiment, the present invention relates to primary terminated polyisobutylene compounds having two or more primary termini selected from amine groups or methacrylate groups.