  Understanding magnetic field strength and morphology is very important for
studying astrophysical jets. Polarization signatures have been a standard way
to probe the jet magnetic field. Radio and optical polarization monitoring
programs have been very successful in studying the space- and time-dependent
jet polarization behaviors. A new era is now arriving with high-energy
polarimetry. X-ray and $\gamma$-ray polarimetry can probe the most active jet
regions with the most efficient particle acceleration. This new opportunity
will make a strong impact on our current understanding of jet systems. This
paper summarizes the scientific potential and current model predictions for
X-ray and $\gamma$-ray polarization of astrophysical jets. In particular, we
discuss the advantages of using high-energy polarimetry to constrain several
important problems in the jet physics, including the jet radiation mechanisms,
particle acceleration mechanisms, and jet kinetic and magnetic energy
composition. Here we take blazars as a study case, but the general approach can
be similarly applied to other astrophysical jets. We conclude that by comparing
combined magnetohydrodynamics (MHD), particle transport, and
polarization-dependent radiation transfer simulations with multi-wavelength
time-dependent radiation and polarization observations, we will obtain the
strongest constraints and the best knowledge of jet physics.
