0νββ decay can determine the mass scale and mass hierarchy of neutrinos, providedthat the corresponding nuclear matrix elements (NMEs) are known. However, thediscrepancy of NMEs from different nuclear models vary up to a factor aroundthree times. In this talk, the uncertainties of NMEs from effective interactions,ground-state correlations, as well as higher-order many-body correlations will bediscussed. I will also talk about the description of the γ decay of giant resonances tolow-lying states, where the particle vibration coupling effect is non-negligible.