Electroweak Baryogenesis and Higgs Physics

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.