  We compare the systematics of the magnetic field geometry in the "red"
low-energy peaked BL Lacs (LBLs) and "blue" high-energy peaked BL Lacs (HBLs)
using VLBI polarimetric images. The LBLs are primarily "radio--selected" BL
Lacs and the HBLs are primarily "X-ray selected". In contrast to the LBLs,
which show predominantly transverse jet magnetic fields, the HBLs show
predominantly longitudinal fields. Thus, while the SED peaks of core-dominated
quasars, LBLs and HBLs form a sequence of increasing frequency, the magnetic
field geometry does not follow an analogous sequence. We briefly investigate
possible connections between the observed parsec-scale magnetic field
structures and circular polarization measurements in the literature on various
spatial scales.
