AUTHOR=Papoulias Dimitrios K. , Kosmas Theocharis S. , Kuno Yoshitaka TITLE=Recent Probes of Standard and Non-standard Neutrino Physics With Nuclei JOURNAL=Frontiers in Physics VOLUME=Volume 7 - 2019 YEAR=2019 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00191 DOI=10.3389/fphy.2019.00191 ISSN=2296-424X ABSTRACT=We review current standard and non-standard neutrino physics probes that are based on nuclear measurements. We pay special attention on the discussion of prospects to extract new physics at prominent rare event measurements looking for neutrino-nucleus scattering, as the coherent elastic neutrino-nucleus scattering that may involve lepton flavour violation (LFV) in neutral currents (NC). For the latter processes several appreciably sensitive experiments, like the COHERENT, MINER, CONUS, TEXONO, RED100 and others, using promising target nuclei are in operation or have been planed to operate in the near future. We also discuss comprehensively phenomenological and theoretical studies, in particular those referred to the nuclear physics aspects and provide useful predictions for the relevant experiments. Furthermore, motivated by the recent discovery of CE$\nu$NS at the COHERENT experiment, we summarize the impact of non-standard interactions and novel vector $Z^\prime$ or scalar $\phi$ mediators to the CE$\nu$NS event rates and provides estimates for the corresponding current and future sensitivities.