© 2019 by Annual Reviews. All rights reserved. Neutrinoless double-beta decay is a forbidden, lepton-number-violating nuclear transition whose observation would have fundamental implications for neutrino physics, theories beyond the Standard Model, and cosmology. In this review, we summarize the theoretical progress to understand this process, the expectations and implications under various particle physics models, and the nuclear physics challenges that affect the precise predictions of the decay half-life. We also provide a synopsis of the current and future large-scale experiments that aim to discover this process in physically well-motivated half-life ranges.