Reflections on the Strong CP Problem
  I discuss how anomalies affect classical symmetries and how, in turn, the non-trivial nature of the gauge theory vacuum makes these quantum corrections troublesome. Although no solution seems in sight for the cosmological constant problem, I examine three possible approaches to the strong CP problem involving vacuum dynamics, an additional chiral symmetry, and the possibility of spontaneous CP or P breaking. All of these "solutions" have their own problems and suggest that, at a deep level, we do not understand the nature of CP violation. Nevertheless, it remains extremely important to search for experimental signals predicted by these theoretical "solutions", like invisible axions. 
R. D. Peccei (University of California, Los Angeles)