A permanent electric dipole moment (EDM) of a particle or system is a separation of charge along its angular-momentum axis and is a direct signal of T-violation and, assuming CPT symmetry, CP violation. For over sixty years EDMs have been studied, first as a signal of a parity-symmetry violation and then as a signal of CP violation that would clarify its role in nature and in theory. Contemporary motivations include the role that CP violation plays in explaining the cosmological matter-antimatter asymmetry and the search for new physics. Experiments on a variety of systems have become ever-more sensitive, but provide only upper limits on EDMs, and theory at several scales is crucial to interpret these limits. Nuclear theory provides connections from Standard-Model and Beyond-Standard-Model physics to the observable EDMs, and atomic and molecular theory reveal how CP-violation is manifest in these systems. EDM results in hadronic systems require that the Standard Model QCD parameter ofθ must be exceptionally small, which could be explained by the existence of axions -also a candidate darkmatter particle. Theoretical results on electroweak baryogenesis show that new physics is needed to explain the dominance of matter in the universe. Experimental and theoretical efforts continue to expand with new ideas and new questions, and this review provides a broad overview of theoretical motivations and interpretations as well as details about experimental techniques, experiments, and prospects. The intent is to provide specifics and context as this exciting field moves forward.

There is strong circumstantial evidence that the shape of atomic nuclei with particular values of Z and N prefers to assume octupole deformation, in which the nucleus is distorted into a pear shape that loses the reflection symmetry of a quadrupole-deformed (rugby ball) shape prevalent in nuclei. Recently, useable intensities of accelerated beams of heavy, radioactive ions have become available at the REX-ISOLDE facility at CERN. This has allowed electric octupole transition strengths, a direct measure of octupole correlations, to be determined for short-lived isotopes of radon and radium expected to be unstable to pear-like distortions. The data are used to discriminate differing theoretical approaches to the description of the octupole phenomena, and also help restrict the choice of candidates for studies of atomic electric-dipole moments, that provide stringent tests of extensions to the Standard Model.

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We have measured the T-odd permanent electric dipole moment of 129Xe with spin exchange pumped masers and a 3He comagnetometer. The comagnetometer provides a direct measure of several systematic effects that may limit electric dipole moment sensitivity, and we have directly measured the effects of changes in leakage current that result when the applied electric field is changed. Our result, d(129Xe) = 0.7+/-3.3(stat)+/-0.1(syst)x10(-27)e cm, is a fourfold improvement in sensitivity.