  This PhD thesis deals with the current experimental hint for large CP
violation in the leptonic sector. We first quantify its global statistical
significance, by combining the results from relevant neutrino oscillation
experiments. As the hint is indirect, other new physics apart from three
massive neutrinos could be present, masking the results as direct leptonic CP
violation has not yet been conclusively observed. Thus, we move on to checking
the robustness of the hint against the framework in which the experimental data
is interpreted; in other words, its physical origin. To that purpose, we
confront with data the scenario that is less bounded by other experiments:
neutral current Non-Standard Interactions (NSI) among neutrinos and matter. In
the end, CP violation induced by neutrino masses and leptonic mixing is found
to be quite robust, due to the large amount of neutrino flavour transition data
collected along three decades.
  Nevertheless, the next generation LBL accelerator experiments are aimed at
precision measurements that could be more severely affected. Luckily, in the
last years the COHERENT experiment has provided independent constraints on NSI.
In the final chapter of the thesis, the data from the COHERENT experiment is
analysed and integrated into the global analyses from previous chapters. These
first results could be greatly improved by increasing the statistics of the
signal and/or by performing measurements with different nuclei sensitive to
different NSI models. For that, the European Spallation Source is an ideal
future facility, whose prospects for bounding NSI are also explored.
  In summary, this thesis takes a global approach to rigorously assess whether
cutting-edge leptonic flavour measurements are pointing towards a new strong
violation of a symmetry of Nature.
