Molecules as diagnostics of solar and stellar magnetic fields

We present an overview of the recent advances in using molecular lines for studying solar and stellar magnetic fields. The synthetic Stokes profiles of various molecular species in the presence of magnetic fields have been compared with profiles observed in sunspots. The agreement between the theory and observations is remarkable. Introducing molecular lines into the inversion of sunspot spectra leads to significant improvements in the deduced magnetic field vector. The high temperature sensitivity of molecular lines allows for high-contrast imaging of small-scale magnetic fields in the solar photosphere and the fine structure of sunspots. Furthermore, the process of coherent scattering in molecular lines in the presence of a magnetic field (the Hanle effect) allows us to investigate spatially unresolved solar magnetic fields. We show also how molecular lines can be used for studying magnetic fields in spatially unresolved spots on the surfaces of cool active stars.