Polyether-epoxide polymer compositions are disclosed. The compositions comprise a reaction product of a polyepoxide compound and a polyol composition comprising a polyether polyol. The ratio of epoxy equivalents to hydroxyl equivalents is within the range of 0.5:1 to 3:1. The polyether-epoxide composition has a Tg within the range of -40°C to 60°C. The polyether polyol has a hydroxyl value within the range of 150 to 800 mg KOH/g and an average hydroxyl functionality within the range of 3.5 to 8.0. In some aspects, the polyol composition further comprises a polyester polyol. Low- and elevated-temperature processes catalyzed by bases or Lewis acids for making the polyether-epoxide compositions are also disclosed. In a simple yet innovative approach, a new class of polymers useful for coatings, elastomers, adhesives, sealants, and other valuable products is assembled from readily available starting materials without reliance on polyamines or polyisocyanates.