Reflections on the strong CP problem

I discuss how anomalies affect classical symmetries and how, in turn, the n on-trivial nature of the gauge theory vacuum makes these quantum correction s troublesome. Although no solution seems in sight for the cosmological con stant problem, I examine three possible approaches to the strong CP problem involving vacuum dynamics, an additional chiral symmetry, and the possibil ity of spontaneous CP or P breaking. All of these "solutions" have their ow n problems and suggest that, at a deep level, we do not understand the natu re of CP violation. Nevertheless, it remains extremely important to search for experimental signals predicted by these theoretical "solutions", like i nvisible axions.