Time-variable polarization is an extremely valuable observational tool to probe the dynamical physical conditions of blazar jets. Since 2008, we have been monitoring the flux and linear polarization of a sample of gamma-ray bright blazars at optical frequencies. Some of the observations were performed on nightly or intra-night time-scales in four optical bands, providing information on the frequency and time dependence of the polarization. The observed behavior is similar to that found in simulations of turbulent plasma in a relativistic jet that contains a standing shock and/or a helical background magnetic field. Similar simulations predict the characteristics of X-ray synchrotron polarization of blazars that will be measured in the future by the Imaging X-ray Polarimetry Explorer (IXPE).