Abstract: For more than two decades, solar, atmospheric, reactor and accelerator neutrino oscillation experiments have provided substantial evidence that neutrinos have mass. However, the Standard Model (SM) of particle physics predicts that the neutrino mass is zero. This indicates that there must be new physics beyond the SM. This article will assess the important implications of neutrinoless double-beta decays for cosmology and the quest for newphysics, especially the unique role that experimental observation of such rare decays plays in the latest research on particle physics and cosmology.