The baryon washout problem of electroweak baryogenesis in the standard Big Bang cosmology can be avoided if inflation does not end before the electroweak scale. I discuss inflationary models in which this is possible and argue that depending on the parameters, the baryon asymmetry can be generated in two different ways: either in a non-thermal phase transition or through the Kibble mechanism. I also present results from non-perturbative numerical simulations of the non-equilibrium dynamics of the electroweak theory after inflation.