  In various extensions of the Standard Model of particle physics, and
intriguingly even in the three-generation Standard Model without neutrino
masses, neutrinos are allowed to have very tiny electric charges. After a
review of the theoretical scenarios that allow the emergence of such charges,
we discuss the existing observational limits and we derive new stringent direct
upper bounds for the charges of the muon and tau neutrinos. We also point out a
flavor-universal lower bound on neutrino charges which is obtained from the
weak gravity conjecture, that is based on the hypothesis that gravity is the
weakest force. We finally present a new flavor-universal upper bound on
neutrino charges based on astrophysical observations of Magnetars.
