  First I will review the QCD theta problem and the Peccei-Quinn solution, with
its new particle, the axion. I will review the possibility of the axion as dark
matter. If PQ symmetry was restored at some point in the hot early Universe, it
should be possible to make a definite prediction for the axion mass if it
constitutes the Dark Matter. I will describe progress on one issue needed to
make this prediction -- the dynamics of axionic string-wall networks and how
they produce axions. Then I will discuss the sensitivity of the calculation to
the high temperature QCD topological susceptibility. My emphasis is on what
temperature range is important, and what level of precision is needed.
