An updated review on theoretical research on the role of magnetic fields in prominences is presented. It is concluded that the theory of the Hanle effect has reached a sufficient degree of sophistication and provides a reliable method for measuring the vector magnetic field. For optically thin lines, insensitive to depolarizing collisions, the theory provides a 'model independent' diagnostic method. The He I D3 line is considered to be particularly suitable for the diagnostics of magnetic fields in prominences, due to the negligibility of optical thickness and its insensitivity to depolarizing collisions. Optically thick lines provide the unique possibility of determining the magnetic field vector from disk observations. Linear polarization observations in H-alpha filaments using new spectropolarimetric instrumentation will make it possible to obtain important information on the magnetic configuration in the higher layers of prominences.