Nuclear Schiff Moments and CP Violation

This paper reviews the calculation of nuclear Schiff moments, which one must know in order to interpret experiments that search for time-reversal-violating electric dipole moments in certain atoms and molecules. After briefly reviewing the connection between dipole moments and CP violation in and beyond the Standard Model of particle physics, Schiff's theorem, which concerns the screening of nuclear electric dipole moments by electrons, Schiff moments, and experiments to measure dipole moments in atoms and molecules, the paper examines attempts to compute Schiff moments in nuclei such as $^{199}$Hg and octupole-deformed isotopes such as $^{225}$Ra, which are particularly useful in experiments. It then turns to ab initio nuclear-structure theory, describing ways in which both the In-Medium Similarity Renormalization Group and coupled-cluster theory can be used to compute important Schiff moments more accurately than the less controlled methods that have been applied so far.