We present some first results of a program to map the distribution of linear polarization in compact radio sources with milliarcsecond resolution. We show first-epoch maps of 3C345 and 0735 + 178 and first- and second-epoch maps of OJ287. In general, the polarization is mainly associated with optically thin (jet) components. In the case of OJ287, polarization maps made 1 year apart are strikingly different. We also discuss some of the theoretical issues raised by these observations.