Abstract: In this talk, I will discuss recent advances on the description of lepton-nucleus interactions using Green’s Function Monte Carlo and the extended factorization scheme, which is based on realistic spectral functions of the nuclear target. A particular emphasis will be placed on the discussion of  theoretical error estimates, which are crucial to meet the goals of guiding and interpreting electron-scattering and accelerator neutrino-oscillation measurements. Finally, I will show results obtained with ACHILLES, a novel lepton event generator.