VLBI observations of blazars provide the closest look at compact jets that are thought to be responsible for the variable emission of blazars from radio to γ-ray wavelengths. It appears that flux variability at different wavelengths is connected to changes in jet structure near its base. The changes happen on timescales of weeks or less, which require frequent VLBI monitoring to follow. Currently, the Very Long Baseline Array is the best tool to perform such observations. Images from the VLBA reveal connections between events in compact jets and behaviour at different wavelengths. Here, I discuss how physical parameters (Lorentz and Doppler factors, viewing and opening angles) of compact jets of blazars can be derived from intense VLBA monitoring at 7 mm, variability of polarization in the core region of parsec scale radio jets, and connections between 7 mm polarization in the VLBI core and polarization at shorter wavelengths.