A number of high priority subjects in astrophysics can be addressed by a state-of-the-art soft x-ray grating spectrometer, such as the role of Active Galactic Nuclei in galaxy and star formation, characterization of the Warm-Hot Intergalactic Medium and the missing baryon problem, characterization of halos around the Milky Way and nearby galaxies, as well as stellar coronae and surrounding winds and disks. An Explorer-scale, largearea (> 1,000 cm2), high resolving power (R =λ/Δλ > 3,000) soft x-ray grating spectrometer is highly feasible based on Critical-Angle Transmission (CAT) grating technology, even for telescopes with angular resolution of 5-10 arcsec. Still, significantly higher performance can be provided by a CAT grating spectrometer on an X-ray- Surveyor-type mission. CAT gratings combine the advantages of blazed reflection gratings (high efficiency, use of higher diffraction orders) with those of conventional transmission gratings (lowmass, relaxed alignment tolerances and temperature requirements, transparent at higher energies) with minimalmission resource requirements. They are high-efficiency blazed transmission gratings that consist of freestanding, ultra-high aspect-ratio grating bars fabricated from silicon-on-insulator (SOI) wafers using advanced anisotropic dry and wet etch techniques. Blazing is achieved through grazing-incidence reflection off the smooth grating bar sidewalls. The reflection properties of silicon are well matched to the soft x-ray band, and existing silicon CAT gratings can exceed 30% absolute diffraction efficiency, with clear paths for further improvement. Nevertheless, CAT gratings with sidewalls made of higher atomic number elements allow extension of the CAT grating principle to higher energies and larger dispersion angles, thus enabling higher resolving power at shorter wavelengths. We show x-ray data from CAT gratings coated with a thin layer of platinum using atomic layer deposition, and demonstrate efficient blazing to higher energies and much larger blaze angles than possible with silicon alone. We also report on measurements of the resolving power of a breadboard CAT grating spectrometer consisting of a Wolter-I slumped-glass focusing mirror pair from Goddard Space Flight Center and CAT gratings, performed at the Marshall Space Flight Center Stray Light Facility. Measurement of the Al Kα doublet in 18th diffraction order shows resolving power > 10,000, based on conservative preliminary analysis. This demonstrates that currently fabricated CAT gratings are compatible with the most advanced grating spectrometer instrument designs for future soft x-ray spectroscopy missions.