  The electromagnetic properties of neutrinos have attracted considerable
attention from researchers for many decades (see [1] for a review). However,
until recently, there was no indication in favour of nonzero electromagnetic
properties of neutrinos either from laboratory experiments with ground-based
neutrino sources or from observations of astrophysical neutrino fluxes. The
situation changed after the XENON collaboration reported [2] results of the
search for new physics with low-energy electronic recoil data recorded with the
XENON1T detector. The results show an excess of events over the known
backgrounds in the recoil energy which, as one of the possible explanations,
admit the presence of a sizable neutrino magnetic moment, the value of which is
of the order of the existing laboratory limitations. In these short notes we
give a brief introduction to neutrino electromagnetic properties and focus on
the most important constraints on neutrino magnetic moments, charge radii and
millicharges from the terrestrial experiments and astrophysical considerations.
The promising new possibilities for constraining neutrino electromagnetic
properties in future experiments are also discussed.
