Along this thesis we address the interaction of neutrinos with nucleons and nuclei, in different scenarios. In first place, we critically analyze a proposal to explain the excess of events in the mini experiment, developed Masip et al. (JHEP 1301, 106 (2013)) and based in a model proposed by Gninenko (Phys. Rev. D83, 015015 (2011)). In this model we have a heavy neutrino, with a mass around 50 GeV, which would be produced in the interaction between the incoming light neutrino and the detector material. Then this heavy neutrino would decay emitting a light neutrino and a photon. The Cherenkov detectors are unable to distinguish a photon signal from an electron one, for this reason this model would be able to explain the anomaly. In our work we describe in detail the heavy neutrino production and its decay. Taking into account the detector parameters we make an estimation of the signal that would be produced in MiniBooNE and we compare it with the excess. The Short-Baseline Neutino Program (SBN) program at Fermilab incorporates a new generation of detectors to make a further study of neutrino oscillations. These experiments shall be able to confirm or discard the MiniBooNE signal. We have also predicted the signal from the heavy neutrino decays, for all the SBN detectors. We have analyzed the nucleon axial form factor, FA, which is not only a fundamental nucleon property but also a source of uncertainty in the amplitudes of the interactions between neutrinos and nucleons and, therefore, in the cross sections. Bubble chamber experiments of neutrino scattering on deuterium collected a data set for the QE process, from which FA can be extracted. For this purpose we have performed a semi-parametric analysis and obtained model-independent information about FA from the ANL experimental data. For the analysis we have used feed-forward neural networks in a multilayer perceptron (MLP) configuration. The tool that allows us to choose between all the different results given by the neural networks is Bayesian statistics. We studied the model proposed by Alam et al. (Phys. Rev. D82, 033001 (2010)) for kaon production in neutrino-nucleon scattering. In this tree-level model, the unitarity of the S matrix is not respected. We have modified this model, by partially restoring unitarity. This has been done by imposing Watson’s theorem to the dominant vector and axial-vector contributions in appropriate angular momentum and isospin quantum number sectors. Finally, we present a deep insight into coherent photon emission mediated by NC. The microscopic model of Wang et al. (Phys. Rev. C 89, 015503 (2014)) considers the neutrino interactions with a nucleon, taking into account the most relevant processes at neutrino energies around 1 GeV. Then a coherent sum over all the nucleons in the nucleus is performed, including the nuclear effects form the medium. While there are experiments with high energy fluxes as MINERνA, were the peak of the medium energy flux is at 6 GeV approximately, the range of validity of the microscopic model is insufficient. To extend this range, we added heavier resonances with invariant masses up to 2 GeV to the calculation, making the model useful for this type of fluxes.