  Neutrino oscillations constitute the first experimental confirmation of new
physics, as they require a new piece that is absent in the Standard Model,
non-zero neutrino masses. Questions such as how these masses are generated or
why they are so small compared to other masses, are still under investigation.
In this thesis, we study radiative neutrino mass models, a class of models
where small neutrino masses are generated naturally, while the energy scale at
which new physics appears is still low enough to be tested by current and
future experiments, offering a falsifiable window to test beyond the Standard
Model physics. In these models, neutrino masses are forbidden at the
tree-level, but allowed at a certain order in loops. Consequently, we get
masses suppressed by loop factors without requiring a large new physics scale
and/or small couplings. In particular, we study the systematic classifications
of the $d=7$ Majorana neutrino mass operator at one-loop order, the Weinberg
operator at three-loop order and the $d=4$ Dirac neutrino mass models at the
two-loop level. We then move to more specific models and mechanisms, analysing
the connection between the generation of radiative neutrino masses and the
stability of dark matter from a model-independent point of view, and examine a
particular realisation of the type-I seesaw which relies on the radiative
generation of Dirac Yukawa coupling. Finally, we analyse the phenomenology of
some of the models discussed in the classifications, as well as a very
particular case of neutrinoless double-$\beta$ decay where electrons are
emitted with opposite chiralities along with a light scalar (Majoron).
