Maleate polyester polyols and coatings made from the polyols are disclosed. The polyester polyols comprise recurring units of (a) a digested thermoplastic polyester or an aromatic dicarboxylate source; (b) a diol; (c) 5 to 95 mole % of an α,β-unsaturated monomer; and (d) 5 to 95 mole % of adipic acid, succinic acid, or a mixture thereof, where the mole % ranges for (c) and (d) are based on the combined molar amounts of (c) and (d). The polyols have hydroxyl numbers within the range of 25 to 450 mg KOH/g, an average of 0.5 to 2.5 reactive unsaturation sites per molecule, and a viscosity less than 1500 cP at 75° C. The polyols are thermally curable or energy-curable. Coatings made from the maleate polyester polyols are also described. Traditional coatings based on polyisocyanates and/or (meth)acrylates can be made, in some cases with improved properties and reduced reliance on the acrylate or isocyanate-based components. Surprisingly, the maleate polyester polyols can also be cured directly using UV to produce coatings under ambient conditions without the need for either acrylic or isocyanate functionality, and this allows coating formulators to reduce cost and more easily achieve regulatory compliance without sacrificing important coating properties. Rigid polyisocyanurate and polyurethane foams produced from the maleate polyester polyols have improved fire retardance.