  The necessary complex structures needed for CP violation are not easy to
generate and, indeed, CP can be a symmetry in higher dimensional theories. In
4-dimensions CP violation argues for the existence of a scalar sector and, in
its simplest manifestation, leads to the CKM model. Further CP violating
phases, from an extended scalar sector, are constrained by the requirement of
having no FCNC. Although new CP violating phases are expected in SUSY
extensions of the SM, the good agreement of data with the CKM model only
provides bounds on these phases. Baryogenesis via leptogenesis requires the
presence of CP violating phases in the neutrino sector. However, the CP phases
likely to be eventually meausured experimentally are not necessarily directly
connected to the ones which drive the leptogenesis.
