  The theoretical and experimental issues relevant to neutrinoless double-beta
decay are reviewed. The impact that a direct observation of this exotic process
would have on elementary particle physics, nuclear physics, astrophysics and
cosmology is profound. Now that neutrinos are known to have mass and
experiments are becoming more sensitive, even the non-observation of
neutrinoless double-beta decay will be useful. If the process is actually
observed, we will immediately learn much about the neutrino. The status and
discovery potential of proposed experiments are reviewed in this context, with
significant emphasis on proposals favored by recent panel reviews. The
importance of and challenges in the calculation of nuclear matrix elements that
govern the decay are considered in detail. The increasing sensitivity of
experiments and improvements in nuclear theory make the future exciting for
this field at the interface of nuclear and particle physics.
