Neutrinoless double-beta decay, if observed, would signal physics beyond the Standard Model that would be discovered at energies significantly lower than those at which the relevant degrees of freedom can be excited. Accurate nuclear structure calculation of the nuclear matrix elements (NME) necessary to analyze the decay rates could be helpful to narrow down the list of competing mechanisms, and to better identify the more exotic properties of the neutrinos. In this paper we present and analyze the status of the NME shell model calculations, and their relevance for discriminating the possible competing mechanisms that may contribute to the neutrinoless double-beta decay process.