  Study of the neutrinoless double beta decay, $0\nu\beta\beta$, includes a
variety of problems of nuclear structure theory. They are reviewed here. The
problems range from the mechanism of the decay, i.e. exchange of the light
Majorana neutrino neutrino versus the exchange of some heavy, so far unobserved
particle. Next, the proper expressions for the corresponding operator are
described that should include the effects of the nucleon size and of the recoil
order terms in the hadronic current. The issue of proper treatment of the short
range correlations, in particular for the case of the heavy particle exchange,
is discussed also. The variety of methods employed these days in the
theoretical evaluation of the nuclear matrix elements $M^{0\nu}$ is briefly
described and the difficulties causing the spread and hence uncertainty in the
values of $M^{0\nu}$ are discussed. Finally, the issue of the axial current
quenching, and of the resonance enhancement in the case of double electron
capture are described.
