We review the use of transmission gratings with grazing-incidence telescopes in celestial X-ray astronomy. Gratings were used on the Einstein Observatory and on EXOSAT, and they are planned for AXAF and SPECTROSAT. We outline the basic properties of transmission grating spectrometers and the use of "phased" gratings to enhance the diffraction efficiency. Gratings are fabricated in a multistep process involving generation of a mask followed by replication into a final grating of the appropriate thickness and material. Special attention is given to the AXAF High Energy Transmission Grating (HETG) being fabricated at MIT. The HETG operates over the range 0.4-8 keV, gives resolving powers of 100-1000, effective areas of 10-300 cm2, and a minimum detectable line flux of 1-10 x 10-6 photons cm -2 s'1. The instrument consists of a single array with two types of grating facets: medium-energy gratings (0.6 pm-period, 0.5 pm-thick silver) mounted behind the outer three AXAF mirrors, and high-energy gratings (0.2 pm-period, 1.0 pm-thick gold) mounted behind the inner three mirrors. The materials and thicknesses are selected to maximize efficiency throughout the energy band. The facets are fabricated at MIT using a process involving X-ray lithography. AXAF will also carry a Low Energy Transmission Grating (LETG) supplied by the Laboratory for Space Research at Utrecht. It uses self-supported grating facets of 1.0 gm period and is optimized for operation down to 80 eV. Both the HETG and LETG disperse the spectrum of a source across either of the AXAF focal-plane/imaging detectors. They are most effective for the study of point sources, but they also give moderate resolution spectra of slightly extended sources and can be used to map the spatial distribution of the line emitting regions.© (1988) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.