  I review the ideas leading to the QCD axion and also comment on the Jarlskog
determinant describing the observed weak CP violation, and the axion-related
Kim-Nilles-Peloso inflation. All of these use pseudoscalars, and the underlying
principle is the discrete gauge symmetry either in the bottom-up or top-down
approaches. Here, the effects of gravity are required to be unimportant in the
low energy effective theory. String compactification is safe from the gravity
spoil of global symmetries and some examples from string compactification are
commented.
