Non-random isobutylene copolymer includes repeat units derived from isobutylene and one or more comonomers selected from isoprene, butadiene, cyclopentadiene, dicyclopentadiene, limonene, substituted styrenes, and C4 to C10 dienes other than isoprene, butadiene, limonene, cyclopentadiene, or dicyclopentadiene, wherein the molar ratio of isobutylene derived repeat units to the comonomer derived repeat units is from 75:1 to 1.5:1. The non-random copolymers have a molecular weight, Mn, of from 200 to 20,000 Daltons and typically have a high double bond content and a high vinylidene double bond content when diene monomers are utilized.