The origin of the matter-antimatter asymmetry in the Universe is a fundamental and unresolved mystery. The creation of the asymmetry requires the violation of charge-parity (CP) symmetry. CP violation in the Standard Model, from the phase of the Cabibbo-Kobayashi-Maskawa (CKM) matrix and the θ term in QCD, is too weak, suggesting the presence of stronger CP violation beyond the Standard Model. Searches for permanent electric dipole moments (EDMs) in nucleons, atoms, and molecules have the potential to discover new CP violation. Such experiments have already imposed stringent constraints on CP-violating phases in beyond-Standard-Model theories, and the next generation of experiments is poised to increase sensitivity by several orders of magnitude. The results of such experiments can determine or tightly constrain the low-energy constants (LECs) associated with nuclear interactions that are odd under parity (P) and timereversal (T) symmetry, which, because of the CPT theorem, is equivalent to CP violation. These interactions are responsible for generating Schiff moments, the nuclear quantities that induce atomic EDMs. At present, however, constraints can carry an uncertainty of more than an order of magnitude, primarily because of uncertainties in nuclear-structure calculations.