Ultraviolet (UV)-curable polyurethane compositions are provided which are made by reacting an isocyanate with an ultraviolet (UV)-curable polyol that is made by co-polymerizing an alkylene oxide, an unsaturated carboxylic acid or anhydride and a hydroxy functional compound and which has an ultra-low level of unsaturation. The inventive ultraviolet (UV)-curable polyurethane compositions may find use in or as coatings, adhesives, sealants, elastomers and the like.