The absence of anti-matter in our universe hints towards new sources of CP violation that are not present in the Standard Model. One possible source of such CP violation could hide in the interactions of the Higgs boson. I will discuss the framework of the Standard Model effective field theory in which such anomalous CP-violating Higgs interactions appear naturally. Footprints of Higgs CP violation can be found in a large variety of experiments at a wide range of energy scales. From low-energy atomic and molecular high-precision experiments, to medium-energy flavor experiments, up to the high-energy frontier at the Large Hadron Collider. I discuss a theoretical framework in which these very different searches can be compared showing that the different searches are complementary.