Double beta decay and neutrino masses

The flux of solar and atmospheric neutrinos has been measured with increasing precision, and offers now direct evidence of the presence of neutrino oscillations between different neutrino flavors. The neutrinoless double beta decay, if detected, would provide the complementary information needed to determine neutrino masses, and would also offer definitive evidence that the neutrino is a Majorana particle. A review is presented on the ongoing and future double-beta-decay experiments, the challenges still present in the calculation of double-beta-decay nuclear matrix elements, and of recent improvements based on the pseudo-SU(3) shell model. (Author)