A process for making polymers of conjugated dienes which contain hydroxyl groups, including highly reactive primary 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 at least 0.1 Meq/g polymer, and(d) reacting the epoxidized polymer with an alcohol having one unprotected hydroxyl group in a solvent in the presence of a Lewis acid selected from the group consisting of MX.sub.n where M is selected from the group consisting of boron, aluminum, iron and tin, and X is a halogen, and organic complexes of such acids.A diene polymer containing 0.01 to 15 Meq/g polymer of hydroxyl group, preferably including highly reactive primary hydroxyl groups, and comprised of ether-alcohol units of the formula ##STR1## where R is selected from the group consisting of alkyl radicals containing up to 10 carbon atoms, monohydric and dihydric alcohol groups and carbonate groups; and R.sub.1 and R.sub.2 are hydrogen or alkyl radicals wherein in (G) only one of R.sub.1 or R.sub.2 is hydrogen.