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