Mildly relativistic, oblique shocks are frequently invoked as possible
sites of relativistic particle acceleration and production of strongly variable, polarized
multi-wavelength emission from relativistic jet sources such as blazars, via diffusive shock acceleration
(DSA). This paper summarizes recent results on a self-consistent coupling of DSA and radiation transfer
simulations in blazar jets. We find that the observed spectral energy distributions (SEDs)
of blazars strongly constrain the nature of the hydromagnetic turbulence responsible for pitch-angle
scattering. Specifically, a strongly energy-dependent pitch-angle mean free path is required. In the
case of low-frequency-peaked blazars, we find that the scaling of the pitch-angle-scattering mean-free-path,
$\lambda_{\rm pas}$ sometimes needs to be as strong as $\lambda_{\rm pas} \propto p^3$, where $p$ is
particle momentum. As our model self-consistently reproduces the relative normalization of thermal
vs. non-thermal particles heated/accelerated at the shock, Compton scattering of an external
radiation field by the thermal population produces a bulk Compton feature in the SED. This
feature is appropriate to model the prominent soft X-ray excess in the SED of the BL Lac object
AO 0235+164, which places additional constraints on the level of hydromagnetic turbulence.
A prediction of this interpretation is that the soft X-ray emission in this soft
excess is expected to be highly polarized.