The electromagnetic properties of neutrinos have attracted considerable attention from researchers for many decades (see \cite{Giunti:2014ixa} 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 \cite{Aprile:2020tmw} 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.