Neutrino-nucleus νA → νA and antineutrino-nucleusνA →νA interactions, when the nucleus conserves its integrity, are discussed with coherent (elastic) and incoherent (inelastic) scattering regimes taken into account. In the first regime the nucleus remains in the same quantum state after the scattering and the cross-section depends on the quadratic number of nucleons. In the second regime the nucleus changes its quantum state and the cross-section has an essentially linear dependence on the number of nucleons. The coherent and incoherent cross-sections are driven by a nuclear nucleon form-factor squared |F | 2 term and a (1−|F | 2 ) term, respectively. One has a smooth transition between the regimes of coherent and incoherent (anti)neutrino-nucleus scattering. Due to the neutral current nature these elastic and inelastic processes are indistinguishable if the nucleus recoil energy is only observed. One way to separate the coherent signal from the incoherent one is to register γ quanta from deexcitation of the nucleus excited during the incoherent scattering. Another way is to use a very low-energy threshold detector and collect data at very low recoil energies, where the incoherent scattering is vanishingly small. In particular, for 133 Cs and neutrino energies of 30-50 MeV the incoherent cross-section is about 15-20% of the coherent one. Therefore, the COHERENT experiment (with 133 Cs) has measured the coherent elastic neutrino nucleus scattering (CEνNS) with the inelastic admixture at a level of 15-20%, if the excitation γ quantum escapes its detection.After Freedman's paper [1] it was confirmed [2-5] that in the Standard Model the cross-section of elastic neutrino scattering off a nucleus is enhanced with respect to neutrino scattering off a single nucleon. The amplification factor for a spinless even-evenHere T A is the kinetic energy of the scattered nucleus, m A is the nucleus mass, q is the momentum transfer, G F is the Fermi constant, Z and N are the numbers of protons and neutrons, g p/n V are the proton/neutron couplings of the nucleon vector current, and F p/n (q) are the proton/neutron form-factors of the nucleus. The form-factors vanish as |q| → ∞ and approach unity (F p/n (q) = 1) if |q|R A 1, where R A is the radius of the nucleus. The coherency requirement reads as |q|R 1. Freedman used the termin "coherent neutrino-nucleus scattering" (CNNS) [1] to emphasize the fact that the dependence of the corresponding cross-section is quadratic in terms of the number of nucleons.The importance of the CNNS was demonstrated for a number of observables in astrophysics, like stellar collapse [13,14], and Supernovae [12,[15][16][17], in studies of physics beyond the Standard Model (SM) [3,11,[18][19][20][21][22][23][24][25][26][27][28], and in investigation of the nuclear structure [4,[29][30][31][32][33]. Due to the neutral-current nature an observation of ν-oscillations with CNNS could be evidence for sterile neutrino(s) [34,35]. Coherent scattering off atomic systems was studied in [36,37]. There are some expe...