The operating principles of several cavities for VUV radiation and soft X-rays (1000 A > l > 1 A) are described. The operation of the cavities is based on grazing-incidence X-ray optics. Some types of ring cavities and a cavity with pear-shaped mirrors are considered, as well as a semi-ring cavity, in which structural X-ray optics is used in addition to the grazing-incidence optics. The performance of the cavities and their efficiency are discussed.