  The violation of CP symmetry is one of Sakharov's conditions for the
matter-antimatter asymmetry of the Universe. Currently known sources of CP
violation in the quark and neutrino sectors are insufficient to account for
this. Is CP also violated in the Higgs sector? Could the SM-like Higgs boson be
a mixture of even and odd CP states of an extended Higgs sector? With what
precision could such effects be measured at future electron-positron colliders?
These questions will be discussed in the light of the latest and ongoing
studies at ILC.
