Neutrinoless double-beta decay is a hypothetical weak-interaction process in which two neutrons inside an atomic nucleus simultaneously transform into protons and only two electrons are emitted. Since the electrons are emitted without accompanying antineutrinos, the process violates the lepton-number conservation and requires that neutrinos are Majorana particles, hence providing unique vistas in the physics beyond the Standard Model of particle physics. The potential to discover new physics drives ambitious experimental searches around the world. However, extracting interesting physics from the experiments relies on nuclear-theory predictions, which remain a major uncertainty.
I will give a review on recent advances in the evaluation of the nuclear matrix elements (NMEs) of neutrinoless double-beta decay. The calculation of the NMEs requires knowledge of both the structure of the involved nuclei and the operators mediating the decay. First, I will review different methods used to solve the nuclear many-body problem and show how nuclear structure can affect the theory predictions of double-beta decays. Then, I will discuss the evaluation of recent effective-field-theory corrections to the double-beta-decay operators and their effect on the theory predictions in medium-heavy to heavy nuclei. I will also discuss how the theory predictions can be constrained by other nuclear observables that can be or have been measured.