In recent years, sensitivity of experimental tests of CP symmetry in flavor-conserving channels has seen a great deal of improvement. Electric Dipole Moments - or EDMs - become a very powerful tool for probing the multi-TeV scale physics. I review the Standard Model expectations for EDMs, including the theta terms and the CKM phase, and discuss the need for improving theoretical predictions in case of theta. I apply null results for EDM experiments to constrain the CP-odd vertices of the Higgs boson, and discuss implications for supersymmetric models.