Observing neutrinoless double-beta (0nbb) decay is the most promising
way to detect lepton number violation in the laboratory, and it would imply
that neutrinos are its own antiparticle. The decay half-life naturally
depends on a nuclear matrix element that needs to be calculated
theoretically. A good knowledge of this matrix element is key for the
planning of 0nbb decay experiments, and also to extract information on
the neutrino mass once 0nbb decay is observed.
At the moment, predicted matrix-element values depend on the
many-body method used to calculate them and, in addition, they may
need to be ”quenched”, as the matrix elements of other beta decays that,
however, have a very different momentum-transfer regime. I will discuss
recent efforts towards obtaining reliable nuclear matrix elements, ranging
from improved calculations with standard many-body approaches, to the
first application of "ab initio" many-body methods to 0nbb decay, finalizing
with possible measurements that could be very useful to test calculations
and to constrain the value of the 0nbb matrix elements.