  A large fraction of the baryons and most of the metals in the Universe are
unaccounted for. They likely lie in extended galaxy halos, galaxy groups, and
the cosmic web, and measuring their nature is essential to understanding galaxy
formation. These environments have virial temperatures >10^5.5 K, so the gas
should be visible in X-rays. Here we show the breakthrough capabilities of
grating spectrometers to 1) detect these reservoirs of hidden metals and mass,
and 2) quantify hot gas flows, turbulence, and rotation around the Milky Way
and external galaxies. Grating spectrometers are essential instruments for
future X-ray missions, and existing technologies provide 50-1500-fold higher
throughput compared to current orbiting instruments.
