  We discuss the constraints on the Higgs sector coming from the requirement of
the generation of the matter-antimatter asymmetry at the electroweak phase
transition. These relate to both a strongly first order first transition,
necessary for the preservation of the generated baryon asymmetry, as well as
CP-violation, necessary for its generation. This scenario may lead to exotic
decays of the Standard Model like Higgs, a deviation of the di-Higgs production
cross section, or CP-violation in the Higgs sector. All these aspects are
expected to be probed by the LHC as well as by electric dipole moment
experiments, among others. Further phenomenological implications are discussed
in this short review.
