Abstract Weak-interaction and nuclear-structure aspects of double beta decay are reviewed. Starting from effective electroweak lagrangians, decay rates for the two-neutrino and neutrinoless modes of the nuclear double beta decay transitions are defined and second-order perturbative expressions for the nuclear decay amplitudes are given. Nuclear matrix elements of the relevant operators are presented, as extracted from data and from shell-model and QRPA calculations as well as from other theoretical approximations. The analysis is performed both for the two-neutrino and neutrinoless modes of the decay. The expressions for ground-state-to-ground-state and ground-state-to-excited-state transitions are presented. Updated experimental and theoretical information on β −β − decays in 48Ca, 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 124Sn, 128Te, 130Te, 136Xe, 150Nd, and on β +β +, β + EC and double EC decays in 78Kr, 92Mo, 96Ru, 106Cd, 124Xe, 130Ba, 136Ce is analyzed and compared with theoretical results. The relevance of single-beta-decay transitions feeding some of the nuclei where double-beta-decay transitions occur is pointed out. The systematics of various phase-space factors and extracted matrix elements is presented.