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After reviewing the origin of the strong CP problem and its phenomenological implications, I will discuss solutions based on Parity (P) or Charge-Parity (CP) symmetry. I will focus on two possibilities that I have recently studied. In the first, P exchanges two copies of the Standard Model (SM), with QCD identified as the diagonal subgroup of the two SU(3) gauge groups, leading to a theory free of the strong CP problem. In the second, CP violation arises solely from a scalar sector with multiple Higgs copies, while a flavor symmetry ensures a natural solution to the strong CP problem, with profound consequences for the flavor sector.