After a brief discussion of baryon and lepton number nonconservation, we review the status of thermal leptogenesis with GUT scale neutrino masses, as well as low scale alternatives with keV neutrinos as dark matter and heavy neutrino masses within the reach of the LHC. Recent progress towards a full quantum mechnical description of leptogenesis is described with resonant leptogenesis as an application. Finally, cosmological B-L breaking after inflation is considered as origin of the hot early universe, generating entropy, baryon asymmetry and dark matter. Here N CS , the Chern-Simons number, is an integer characterizing the sphaleron gauge field configuration. At high temperatures, between the critical temperature T EW of the electroweak phase transition and a maximal temperature T S PH ,these processes are believed to be in thermal equilibrium [3]. Although uncontroversial among theorists, it has to be stressed that this important phenomenon has so far not been experimentally tested! It is therefore very 1 Talk given at the XXV International Conference on Neutrino Physics and Astrophysics, June 3-9, 2012, Kyoto, Japan Figure 1: One of the 12-fermion processes which are in thermal equilibrium in the high-temperature phase of the Standard Model.interesting that the corresponding phenomenon of chirality changing processes in strong interactions might be observable in heavy ion collisions at the LHC [4,5].Sphaleron processes relate baryon and lepton number and therefore strongly affect the generation of the cosmological baryon asymmetry. Analyzing the chemical potentials of quarks and leptons in thermal equilibrium, one obtains an important relation between the asymmearXiv:1210.7758v1 [hep-ph]