Polymerized 1,3-butadiene, including styrenic block copolymers, are functionalized with both carboxylic ester groups and ketone linking groups by reaction with carbon monoxide and an alcohol. Such conjugated diene polymers can be reacted in the presence of a catalyst composition that includes a cobalt compound and an amine ligand. The functionalized 1,3-butadiene polymers may be hydrogenated with a nickel/aluminum catalyst which removes olefinically unsaturated carbon-carbon bonds without substantially hydrogenating the ketone linking groups and carboxylic ester groups.