Permanent electric dipole moments (EDMs) are sensitive probes of the symmetry structure of elementary particles, which in turn is closely tied to the baryon asymmetry in the universe. A meaningful interpretation framework for EDM measurements has to be based on effective quantum field theory. We interpret the measurements performed to date in terms of a hadronic-scale Lagrangian, using the SFitter global analysis framework. Part of this Lagrangian is constrained very well, while some of the parameters suffer from too few high-precision measurements, theory uncertainties lead to weaker model constraints, but can be controlled within the global analysis.