Aspects of Soft and Spontaneous CP Violation

We study four different models for CP violation: the standard (KM) model, the aspon model of spontaneous breaking and two models of soft breaking. In all except the standard model, the strong CP problem is addressed and solved. Testable predictions for the area of the unitarity triangle and for (epsilon'/epsilon)_K are emphasized. The issue of CP violation may well become the first place where the standard model of particle theory is shown definitively to be deficient. There are two reasons for expecting this to happen: (1) the strong CP problem is still not understood in the unadorned standard model and (2) the KM mechanism, although unquestionably present, may not provide the full explanation of epsilon_K and (epsilon'/epsilon)_K.