A process for making polymers of conjugated dienes which contain hydroxyl groups in the diene blocks which comprises(a) making a precursor polymer by polymerizing at least one conjugated diene which leaves 1,2 disubstituted, 1,1 disubstituted, 1,1,2 trisubstituted or tetrasubstituted olefinic unsaturation in the polymer,(b) optionally partially hydrogenating said precursor polymer,(c) epoxidizing said precursor polymer such that epoxy groups form at said substituted sites and the amount of epoxy functionality in the polymer is from 0.1 to 5 Meq/g polymer, and(d) reacting the epoxidized polymer with an alcohol solution of hydrochloric acid.A diene polymer containing 0.1 to 10 Meq/g polymer of hydroxyl group and comprised of alcohol units of the formula ##STR1## where R.sub.1 and R.sub.2 are hydrogen or alkyl radicals and X and X' are either --OH or --Cl and at least one of them is --OH.