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The last decades have witnessed the emergence of the basic model of theoretical nuclear physics, which is aimed at understanding how nuclei emerge from the interactions among protons and neutrons. Effective field theories exploit the symmetries of quantum chromo-dynamics to systematically construct realistic nuclear potentials and consistent electroweak currents. They are the input to “ab-initio” many-body methods, aimed at solving the many-body Schrödinger equation with controlled approximations. Among them, quantum Monte Carlo approaches are known for their accuracy and their capability of dealing with short-range nuclear dynamics. I will report on recent quantum Monte Carlo progresses towards a comprehensive description of the spectrum and electroweak interactions of light nuclei, and the nucleonic matter equation of state. The impact of these calculations on accelerator-neutrino oscillation program will be discussed.