Abstract
The strong CP-violating θ parameter, the problem of strong CP violation and their status are reviewed. Among all possibilities, two natural solutions to the strong CP puzzle are thoroughly discussed and emphasized: the axion-type mechanism for hard CP violation and the non-Peccei-Quinn scheme for spontaneous CP nonconservation. Basic properties of the axion are derived from the modified Peccei-Quinn symmetry. Astrophysical and cosmological constraints are described for two different types of invisible axions. In nonaxion solutions, CP is spontaneously broken at the grand-unification scale and the CP phase is transmitted down to the low energy sector by quantum effects or by fermion mixing effects. As a by-product, the cosmological baryon asymmetry, which is caused by the same source of CP violation ultimately responsible for the kaon ε parameter, is generated adequately at the one-loop level.
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