Throughout our universe ubiquitous plasmas emit and absorb at characteristic wavelengths and line intensity ratios that allow us to diagnose and map the physical conditions across a vast range of length scales and densities from the Cosmic Web to the atmospheres of stars.  For example, astronomers believe the majority of baryonic matter in the universe to be “hidden” in hot plasmas too faint to detect with current instruments. The high temperatures of these plasmas lead to highly ionized states of many of the most abundant “metals” (O, C, Ne, Fe, N, Si, Mg, S).  Many of their characteristic lines lie in the soft x-ray band between ~1 and 5 nm wavelength (~0.25 and 1.25 keV in photon energy), where high resolving power is best achieved using grating spectrographs.  However, higher resolving power and larger effective area than those provided by current missions such as XMM-Newton or Chandra are required in order to make progress.  Recently developed critical-angle transmission (CAT) gratings combine the advantages of traditional transmission gratings (relaxed alignment tolerances, low mass, transparency at higher energies) and blazed reflection gratings (high diffraction efficiency, high resolving power due to blazing into high orders) and promise vastly improved figures of merit.  CAT gratings feature freestanding, ultra-high aspect-ratio grating bars with nm-smooth sidewalls and are fabricated from silicon-on-insulator wafers using techniques from the semiconductor and MEMS industries.  A hierarchy of integrated support structures enables the fabrication of > 10 cm² gratings with 200 nm period with a resolving power R = l/Dl > 10000.  CAT grating spectrographs have been proposed for the Arcus and Lynx mission concepts, with effective area up to 4000 cm² and R ~ 7500, which will represent a leap in capabilities of up to two orders of magnitude over current observatories.