  The motivation for the search for $0\nu\beta\beta$ decay is briefly reviewed.
It is stressed that the exchange of light Majorana neutrinos is not the only
possible mechanism of the decay. The link between lepton number and lepton
flavor violation is described and its role in elucidating the
$0\nu\beta\beta$-decay mechanism is discussed. The main topic of the talk is
the evaluation of the nuclear matrix elements and their uncertainty. Various
physics effects that influence the value of the matrix elements are described
and the results of the two main methods, the quasiparticle random phase
approximation and the nuclear shell model, are compared.
