  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.
