Abstract: Accurate predictions of neutrino-nucleus interactions are essential to long-baseline neutrino-oscillation programs. Achieving a comprehensive description in the broad range of energy relevant for neutrino oscillation experiments is a formidable nuclear- and particle-theory challenge. I will focus on our latest results for lepton-nucleus scattering cross sections obtained within nuclear many-body methods relying on accurate models of nuclear dynamics. The Green’s Function Monte Carlo approach allows to provide virtually exact electroweak responses of nuclei up to A=12 in the quasi-elastic region. I will present electron–⁴He cross sections for a variety of kinematical setups and show preliminary results for the electroweak charged-current responses and muon capture on light nuclei. Then, I will outline the formalism based on the impulse approximation and spectral function. In particular, I will present the results we obtained for electromagnetic and charged-current scattering processes off ¹²C. The role played by relativistic two-body electroweak current operators and the pion-production mechanisms, included for the first time in our calculations, will be also discussed in detail.  Finally, I will briefly show a comparison with the data of the E12-14-012 experiment at Jefferson Lab Hall A for inclusive electron scattering on $^40$ Ar and natural titanium targets at a fixed beam energy and scattering angle. Our calculations have been obtained using the spectral functions of argon and titanium computed within a state- of-the-art ab initio theory.