  We discuss the use of comagnetometry in studying new physics that couples to
fermionic spin. Modern comagnetometry is -- in absolute energy units -- the
most sensitive experimental technique for measuring the energy difference
between quantum states, reaching sensitivities in the $10^{-26}\,$eV range. The
technique suppresses the magnetic interactions of the spins, making searches
for non-standard-model interactions possible. Many implementations have been
developed and optimized for various uses. New physics scenarios which can be
probed with comagnetometers include: EDMs, violations of Lorentz invariance,
Goldstone bosons of new high-energy symmetries, CP-violating long-range forces,
and axionic dark matter. We consider the prospects for improvements in the
technique, and show -- based purely on signal-to-noise ratio with existing
technology -- that there is room for several orders of magnitude in further
improvement. We also evaluate several sources of systematic error and
instability that may limit improvements.
