  Neutrino oscillations physics is entered in the precision era. In this
context accelerator-based neutrino experiments need a reduction of systematic
errors to the level of a few percent. Today one of the most important sources
of systematic errors are neutrino-nucleus cross sections which in the
hundreds-MeV to few-GeV energy region are known with a precision not exceeding
20%. In this article we review the present experimental and theoretical
knowledge of the neutrino-nucleus interaction physics. After introducing
neutrino oscillation physics and accelerator-based neutrino experiments, we
overview general aspects of the neutrino-nucleus cross sections, both
theoretical and experimental views. Then we focus on these quantities in
different reaction channels. We start with the quasielastic and
quasielastic-like cross section, putting a special emphasis on multinucleon
emission channel which attracted a lot of attention in the last few years. We
review the main aspects of the different microscopic models for this channel by
discussing analogies and differences among them.The discussion is always driven
by a comparison with the experimental data. We then consider the one pion
production channel where data-theory agreement remains very unsatisfactory. We
describe how to interpret pion data, then we analyze in particular the puzzle
related to the impossibility of theoretical models and Monte Carlo to
simultaneously describe MiniBooNE and MINERvA experimental results. Inclusive
cross sections are also discussed, as well as the comparison between the
$\nu_\mu$ and $\nu_e$ cross sections, relevant for the CP violation
experiments. The impact of the nuclear effects on the reconstruction of
neutrino energy and on the determination of the neutrino oscillation parameters
is reviewed. A window to the future is finally opened by discussing projects
and efforts in future detectors, beams, and analysis.
