Several experiments proved that the neutrinos are not massless, their extreme lightness, however, represents a great puzzle for theoreticians. It is speculated that the smallness of neutrino masses can be related to some kind of physics beyond the Standard Model of particle physics. Different mechanisms of this type will be discussed and a particular model which relates the smallness of neutrino masses to another puzzle of today's particle physics, the so-called dark matter, will be presented.