We review observational evidence for a matter–antimatter asymmetry in the early universe, which leads to the remnant matter density we observe today. We also discuss bounds on the presence of antimatter in the present-day universe, including the possibility of a large lepton asymmetry in the cosmic neutrino background. We briefly review the theoretical framework within which baryogenesis, the dynamical generation of a matter–antimatter asymmetry, can occur. As an example, we discuss a testable minimal particle physics model that simultaneously explains the baryon asymmetry of the universe, neutrino oscillations and dark matter.