AUTHOR=Rocco Noemi TITLE=Ab initio Calculations of Lepton-Nucleus Scattering JOURNAL=Frontiers in Physics VOLUME=Volume 8 - 2020 YEAR=2020 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00116 DOI=10.3389/fphy.2020.00116 ISSN=2296-424X ABSTRACT=The advent of high precision measurements of neutrinos and their oscillations calls for accurate predictions of their interactions with nuclear targets utilized in the detectors. Over the past decade, ab initio approaches have reached the degree of maturity needed to describe lepton-nucleus scattering processes starting from a realistic model of the interactions among the nucleons and between them and the beam particle. Achieving a comprehensive description of the different reaction mechanisms active in the broad range of energy relevant for oscillation experiments required the introduction of controlled approximations of the nuclear many-body models. In this review, we give an overview of recent developments in the description of electroweak interactions within different approaches and discuss the future perspectives to support the experimental effort in this new precision era.