Layered synthetic microstructure (LSM) x-ray optics may be used to couple a conventional glancing incidence x-ray mirror to a high sensitivity x-ray detector. The LSM mirror is a thin-film multilayer optic that effectively reflects only narrow spectral slices of the incident radiation by Bragg diffraction. By the use of figured LSM optics, it is possible to magnify the x-ray image produced by the primary mirrors so as to maintain their high inherent spatial resolution when used with currently available solid-state detectors. The results of theoretical design and analysis studies of several Spectral Slicing X-Ray Telescope (SSXRT) systems utilizing LSM mirrors figured as hyperboloids, spheres, ellip-soids, and constant optical path aspheric elements are presented. The rms spot size and point response function calculations are given for telescopes in which the LSM optics are designed to yield magnifications of 2 X, 6 X, and 8 X. The results of tilt and decentration studies are discussed. It has been demonstrated that the off-axis optical performance of the SSXRT is superior to that produced by the conventional glancing incidence primary mirror alone. The Stanford/Marshall Space Flight Center Rocket X-Ray Telescope, which will utilize normal incidence LSM optics to couple a Wolter-Schwarzschild primary mirror to high resolution detectors for solar x-ray/EUV studies, is briefly discussed.