Abstract: As one of the rarest processes in nature, neutrinoless double-beta decay is the key in our search for new physics beyond the Standard Model, where we are facing big challenges, both theoretically and experimentally. The precise prediction for this process relies heavily on the nuclear many-body approaches which still lack necessary precision. Results from various methods differ; they can be explained qualitatively but require quantitative investigation. Another great challenge is to determine the underlying mechanisms with only limited observables—chiefly, the properties of emitted electrons and final nuclei—and research in this area is still inadequate.