What do we know about neutrinoless double-beta decay nuclear matrix elements?

Abstract: The detection of neutrinoless double-beta decay will establish the Majorana nature of neutrinos. In addition, if the nuclear matrix elements of this process are reliably known, the experimental lifetime will provide precious information about the absolute neutrino masses and hierarchy. I review the status of nuclear structure calculations for neutrinoless double-beta decay matrix elements, and discuss some key issues to be addressed in order to meet the demand for accurate nuclear matrix elements.