Weak-interaction observables from nuclear-structure calculations of 0νββ decay transitions

The present status of the calculation of the nuclear matrix elements associated with neutrinoless double-beta decay is discussed. The currently available approaches, as well as the historical perspective, are presented in this review. The discussion is restricted to nuclear matrix elements relevant in the context of the light Majorana-neutrino-mediated decays to the ground state and excited states of the final nucleus. Special emphasis is laid on the quantitative description of the 0νββ decay transitions to the excited 0+ states, a subject of very recent interest in the double-beta community.