First I briefly review how the matter-antimatter asymmetry could have been created in the early Universe. Then I focus on a particular mechanism, called leptogenesis, where an asymmetry is created in the decays of heavy right-handed neutrinos. Before the right-handed neutrions could decay they must have been produced, which is the main topic of my talk. They can be produced both by decay or inverse decay and by scattering processes. I show that multiple scattering mediated by soft gauge boson exchange also contributes to the production rate at leading order and gives a strong enhancement.