We discuss the generation of the baryon asymmetry by a strong first order electroweak phase transition in the early universe, particularly in the context of the MSSM. This requires a thorough numerical treatment of the bubble wall profile in the case of two Higgs fields. CP violating complex particle masses varying with the Higgs field in the wall are essential. Since in the MSSM there is no indication of spontaneous CP violation around the critical temperature (contrary to the NMSSM) we have to rely on standard explicit CP violation. Using the WKB approximation for particles in the plasma we are led to Boltzmann transport equations for the difference of left-handed particles and their CP conjugates. This asymmetry is finally transformed into a baryon asymmetry by out of equilibrium sphaleron transitions in the symmetric phase. We solve the transport equations and find a baryon asymmetry depending mostly on the CP violating phases and the wall velocity.
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