Neutrino-nuclear responses associated with astro-neutrinos, single beta decays and double beta decays are crucial in studies of neutrino properties of interest for astro-particle physics. The present report reviews briefly recent studies of the neutrino-nuclear responses from both experimental and theoretical points of view in order to obtain a consistent understanding of the many facets of the neutrino-nuclear responses. Subjects discussed in this review include (i) experimental studies of neutrino-nuclear responses by means of single beta decays, charge-exchange nuclear reactions, muon-photon-and neutrino-nuclear reactions, and nucleon-transfer reactions, (ii) implications of and discussions on neutrino-nuclear responses for single beta decays, for astroneutrinos, and for astro-neutrino nucleosynthesis, (iii) theoretical aspects of neutrino-nuclear responses for beta and double beta decays, for nuclear muon capture and for neutrino-nucleus scattering, and (iv) critical discussions on nucleonic and non-nucleonic spin-isospin correlations and renormalization (quenching or enhancement) effects on the axial weak coupling. Remarks are given on perspectives of experimental and theoretical studies of the neutrino-nuclear responses and on future experiments of double beta decays.