An X-ray generating apparatus generates X-rays from plasma formed by irradiating a laser beam to a target. The apparatus includes an X-ray transmitting film disposed at at least one side of the target with a predetermined gap provided therebetween. The X-ray transmitting film has a thickness such that the film is not broken due to an action in the X-ray generating process. The X-rays are taken out through the X-ray transmitting film. An X-ray microscope can employ such an X-ray generating apparatus, with the X-rays from the apparatus being guided to the sample, with the sample to be observed being disposed in the vicinity of the X-ray transmitting film, and with a detecting device for detecting an X-ray image formed by X-rays transmitted through the sample.