The present invention is directed to polyphenolic polymers formed from dihydroxybenzoic acid (DHB) derivatives or from resorcinol derivatives, monomers which form such polymers, blends of the polymers with drugs and/or additional polymers, as well as medical devices formed from, coated with, impregnated by or coverings made with any of the foregoing polymers (with or without drugs) or blends (with or without drugs).