The last decades brought impressive progress in synthesizing and studying properties of nuclides located very far from the beta stability line. Among the most fundamental properties of such exotic nuclides, the ones usually established first are the half-life, possible radioactive decay modes, and their relative probabilities. When approaching limits of nuclear stability, new decay modes set in. First, beta decays are accompanied by emission of nucleons from highly excited states of daughter nuclei. Second, when the nucleon separation energy becomes negative, nucleons start being emitted from the ground state. A review of the decay modes occurring close to the limits of stability is presented. The experimental methods used to produce, identify, and detect new species and their radiation are discussed. The current theoretical understanding of these decay processes is reviewed. The theoretical description of the most recently discovered and most complex radioactive process—the two-proton radioactivity—is discussed in more detail.

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