Abstract: The status of research on X-ray astronomical telescopes is reviewed. There are six types of such telescopes currently in use in outer space, the simple collimated, encoded aperturee, normal incidence period-multilayer, grazing incident single coating, grazing incident aperiod-multilayer and lobster eye. The principle, features and application of these telescopes are introduced in detail. All these telescopes are complementary to each other. The development of X-ray telescopes and future research in China are discussed.