Currently, the Standard Model of particle physics (SM) is the best theory we have to describe particles and their interactions. However, there is evidence of physics beyond it, which motivates us to seek for a more complete theory. Neutrino oscillations constitute the first experimental confirmation of new physics, as they require a new piece that is absent in the SM, non-zero neutrino masses. Neutrino masses brought new theoretical challenges, for instance questions as how these masses are generated or why are they so small compared to other masses, are still under investigation. In this thesis, we aim to 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 testable at current and future experiments. In these models, neutrino masses are forbidden at the tree-level, but allowed at a certain order in loops. Consequently, one get masses suppressed by loop orders without requiring a large new physics scale and/or small couplings. In the thesis, after providing some brief introduction to neutrino physics and reviewing some of the most important neutrino mass mechanisms, we study several systematic classification of radiative neutrino mass models. Chapter 3 contains the classification of dimension 7 Majorana neutrino mass models generated at one-loop order, in Chapter 4 we study systematically the decomposition of the Weinberg operator at three-loop order, while in Chapter 5 we study the generation of dimension four Dirac neutrino mass models at the two-loop level. We then move to more specific models and mechanisms in Chapters 6 and 7. In the former, we study the connection between the generation of neutrino masses and the stability of dark matter analysing the breaking pattern of lepton number. In Chapter 7 we study, from a model-independent point of view, a particular realisation of the type-I seesaw which relies on the radiative generation of neutrino Dirac couplings. Finally, we end with the phenomenological analysis of some of the models discussed in the previous chapters. Chapters 8 and 9 are devoted to the phenomenological analysis of dimension 7 one-loop neutrino mass models and three-loop neutrino mass models, respectively, while in Chapter 10 we discuss a very particular case of neutrinoless double-β decay where electrons are emitted with opposite chiralities along with a light scalar (Majoron). Summing up, in this thesis we present and discuss a great variety of radiative neutrino mass models from a model-building and phenomenological point of view. We classify them and analyse specific scenarios or models we found particularly interesting due to their phenomenology and/or simplicity. In most of the cases, radiative models can explain the smallness of neutrino masses (and other drawbacks of the Standard Models) with a relative low energy scale, which can be tested by current and future experiments, offering a falsifiable window to new physics.