Radiopaque, iodinated, absorbable polyesters, polyester urethanes, and polyether-ester-urethanes with and without inorganic iodide micro-/nanoparticles dispersed or solubilized therein, and composite inorganic iodide micro-/nanoparticles in an absorbable polyester, polyester-urethane, polyester-ester, or polyether-ester urethane matrix are employed in medical devices and therapeutic compositions.