Multiwavelength polarimetry has become a key tool for probing blazar jet physics, especially with the launch of the Imaging X-ray Polarimetry Explorer (IXPE). I will discuss the polarization properties of High-Synchrotron Peaked (HSP) blazars, where both optical and X-ray emission arise from synchrotron radiation produced by non-thermal electrons. I will show that, regardless of jet magnetization and particle acceleration mechanism, the polarization degree (Pi) depends strongly on the spectral slope of the emitting electrons, whereas the Electric Vector Position Angle (EVPA) is nearly constant. I will present an axisymmetric, stationary model of Poynting-dominated jets where the electromagnetic fields are fully ordered (i.e., non-turbulent). The electromagnetic fields are determined by the jet shape, which in turn depends on the pressure profile of the external confining medium. When the jet shape is quasi-parabolic, the X-ray polarization degree is much higher than the optical one (Pi_X/Pi_O > 2), whereas the EVPA is weakly dependent on the observed frequency. These results compare very well with observations of HSP blazars. Thus, current IXPE data are less sensitive to the specific particle acceleration process than previously thought. I will then discuss polarization variability using a geometric and deterministic model in which off-axis, compact emitting features (i.e., blobs) propagate along the jet with the local flow velocity. The dynamics of the blobs is determined by jet electromagnetic fields, which are calculated self-consistently using the analytical jet model described above. I will show that polarization variability is not universal and depends on the initial conditions of the blobs and on the geometry of the jet, allowing both smooth and irregular changes in the polarization degree and EVPA. My results show that constraining the particle acceleration mechanism from multifrequency polarimetry is extremely challenging.