The experimental observation of neutrino oscillations profoundly impacted the physics of neutrinos, from being well understood theoretically to requiring new physics beyond the standard model of particle physics. Indeed, the mystery of neutrino masses implies the presence of new particles never observed before, often called sterile neutrinos, as they would not undergo standard weak interactions. And while neutrino oscillation measurements entered the precision era, reaching percentlevel precision, many experimental results show significant discrepancies with the standard model, at baselines much shorter than typical oscillation baselines. Such experimental measurements include LSND, MiniBooNE, gallium experiments, and reactor antineutrino measurements. These short baseline anomalies seem to be explainable by the addition of a light sterile neutrino, with mass in the 1 − 10 eV range. However, this hypothesis is in strong tension with many null experimental observations. Other explanations that rely on models containing sterile states with masses in the 1 − 500 MeV could resolve the tension. In this thesis, we test both classes of models. On the one hand, we look for datasets collected at a short baseline which can constrain heavy sterile neutrino models. We find that the minimal model is fully constrained, but several extensions of this model could weaken the current constraint and be tested with current and future datasets. On the other hand, we test the presence of neutrino oscillations at short baselines, induced by a light sterile state, with the data collected by the MicroBooNE experiment, a liquid argon time projection chamber specifically designed to resolve the details of each neutrino interaction. We report null results from both analyses, further constraining the space of possible explanations for the short baseline anomalies. If new physics lies behind the short baseline anomaly puzzle, it is definitely not described by a simple model.