The Standard Model of particle physics is regarded as one of the most successful theories ever developed, offering an incredibly precise understanding of the subatomic world. Nevertheless, despite its remarkable success, this model fails at explaining certain crucial experimental observations, which highlights the need of extending the model. Arguably the most notable issue within this framework is its prediction that neutrinos are massless, contradicting the findings of neutrino flavor oscillation experiments. Moreover, other anomalies are indicating the potential presence of new physics, such as the long-standing discrepancy between the Standard Model predictions for the electron and muon anomalous magnetic moments and their actual measured values, inconsistencies between theoretical predictions and experimental measurements in B-meson decay observables, or the enigmatic nature of Dark Matter. Consequently, it is particularly appealing to connect the underlying mechanisms responsible for neutrino mass and mixing generation to other unresolved questions also deserving attention. Part of this thesis was devoted precisely to this objective. Within its pages, different neutrino mass models were proposed to accommodate different anomalies, studying the possible Lepton Flavor Violating signatures. Additionally, this thesis presented several novel variants of the well-known Scotogenic model from a model-building perspective. Lastly, a comprehensive discussion was provided on how the existing experimental constraints on the parameter space of hypothetical Heavy Neutral Leptons could be reinterpreted in more realistic scenarios rather than the ones considered by most of the experimental collaborations.