Neutrino-nucleus modeling occupies an important place in the neutrino oscillation programme, since it is essential for the precise reconstruction of neutrino energy. Due to nuclear effects, theoretical uncertainties stemming from neutrino-nucleus cross sections largely contribute to the overall systematic errors of oscillation experiments.

We present an overview of challenges which we encounter in this field, paying attention to the ones which are motivated by the Monte Carlo (MC) generator studies. Next, we make a survey of various theoretical models, sketching the main differences between them. We organize the discussion according to the physical mechanisms which give contributions to the total cross section of the neutrino-nucleus scattering, starting from the giant resonances, through the QE excitation, multinucleon knockout, pion production, up to the DIS region.