Blazars whose synchrotron spectral energy distribution (SED) peaks at X-ray energies need to accelerate electrons to energies in the >100 GeV range in relativistic plasma jets at distances of parsecs from the central engine. Compton scattering by the same electrons can explain high luminosities at very high photon energies (>100 GeV) from the same objects. Turbulence combined with a standing conical shock can accomplish this. Such a scenario can also qualitatively explain the level and variability of linear polarization observed at optical frequencies in these objects. Multi-wavelength polarization measurements, including those at X-ray energies by the Imaging X-ray Polarimetry Explorer (IXPE), find that the degree of polarization is several times higher at X-ray than at optical wavelengths, in general agreement with the turbulence-plus-shock picture. Some detailed properties of the observed polarization can be naturally explained by this scenario, while others pose challenges that may require modifications to the model.