The experimental evidences of neutrino oscillation, caused by non-zero neutrino masses and neutrino mixing, which were obtained in the experiments with solar, atmospheric, accelerator and reactor neutrinos, opened new field of research in elementary particle physics. The principal goal is to understand at fundamental level the mechanism giving rise to non-zero neutrino masses and neutrino mixing. The open fundamental questions include those of the nature \u2014 Dirac or Majorana \u2014 of massive neutrinos, of the type of spectrum neutrino masses obey, of the status of CP symmetry in the lepton sector, of the absolute scale of neutrino masses, and more generally, of understanding the origin of flavour in particle physics. The smallness of neutrino masses suggests that their values are related to the existence of a new fundamental mass (energy scale) in particle physics, i.e., to New Physics beyond that predicted by the Standard Theory. The New Physics can manifest itself in the Majorana nature of massive neutrinos, in the existence of sterile neutrinos with masses at the eV scale, in the existence of new non-standard interactions (NSI) of neutrinos, etc. The present Ph.D. thesis explores aspects of this neutrino-related New Physics. More specifically, we first employ the discrete flavour symmetry approach i) to construct a self-consistent theory of lepton flavour, ii) to understand the pattern of neutrino mixing and to describe it quantitatively, and iii) to derive predictions for leptonic Dirac CP violation. Next we investigate the effects of existence of sterile neutrinos with a Majorana mass at the eV scale on the predictions for the neutrinoless double beta decay effective Majorana mass. Further we present a possible interpretation of the results of the reactor neutrino and accelerator experiments (Daya Bay, RENO, Double Chooz and T2K) on the reactor angle \u3b813 in the neutrino mixing matrix in terms of non-standard interactions (NSI) of neutrinos. We also analyse the signatures of sterile neutrinos in reactor antineutrino experiments and, in particular, constrain the active-sterile mixing angle using the high-precision data of the Daya Bay reactor experiment. We finally investigate the impact of sterile neutrinos on precision measurements of the standard neutrino oscillation parameters in the upcoming neutrino experiment JUNO
