  The simplest possibility to generate small Majorana neutrino masses is the
seesaw mechanism. However, the smallness of the observed neutrino masses can
also be understood, if neutrino masses are generated by higher-dimensional
operators and/or at higher loop level. In this talk recent work on systematic
classifications of higher-dimensional and radiative neutrino mass models is
summarized. Two particular classes of special genuine loop diagrams, i.e.
diagrams which can lead to genuine neutrino mass models only under some
specific, well-defined conditions, are also discussed.
