  The status of the theoretical description of neutrino-nuclear interaction for
low and intermediate energies is reviewed and its result compared with the
existing data. Particular emphasis is on $^{12}$C, the ingredient of liquid
scintillator, and on $^{16}$ the main component of the water \v{C}erenkov
detectors. First, I show that the data on the exclusive process populating the
ground state of $^{12}$N are well reproduced by the theory. This is also the
case for the excitation of the continuum with low energy neutrinos from the
muon decay at rest and for the muon capture. However, for not yet understood
reasons, the theory overestimates the cross section for higher energy neutrinos
from the pion decay in flight, by up to 50%. I also show that the Continuum
Random Phase Approximation and the Relativistic Fermi Gas model give very
similar full and differential cross sections for the neutrino energies of
several hundred MeV, thus checking one method against the other.
