  The last decades brought an 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, usually established first,
is 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 become accompanied by emission of nucleons from
highly excited states of daughter nuclei. Second, when the nucleon separation
energy becomes negative, nucleons start to be emitted from the ground state.
Here, we present a review of the decay modes occurring close to the limits of
stability. 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 overviewed. The theoretical
description of the most recently discovered and most complex radioactive
process - the two-proton radioactivity - is discussed in more detail.
