What is the nature and mass of the neutrino? Why is there an abundance of matter over antimatter in our universe? And what is dark matter, anyway? Strangely enough, answers might well lie, yet undiscovered, in an impossibly rare nuclear decay, infinitely subtle moments of a nucleus embedded in a radioactive molecule, or the faintest recoil of a nucleus colliding with dark matter. As the role of atomic nuclei in unraveling such fundamental mysteries continues to deepen, first-principles quantum simulations, beginning from only the underlying nuclear/weak forces, are currently undergoing nothing short of a revolution. In my talk I will outline this modern "ab initio" approach and spotlight several recent milestones in nuclear structure/astrophysics, including statistical predictions for the limits of nuclei as well as the neutron skin of 208Pb to constrain neutron star properties. I will then discuss how parallel advances are driving first predictions of neutrinoless double-beta decay, WIMP-nucleus scattering, and symmetry-violating moments, with quantifiable uncertainties, for essentially all nuclei relevant in searches for new physics.