  Understanding axion cosmology has important experimental consequences since
it constrains the range of allowed values for the axion mass. In the standard
thermal scenario, which assumes Peccei-Quinn symmetry restoration after
inflation, an axion string network forms at the phase transition $T\sim\fa$ and
then radiatively decays into a cosmological background of axions. Under
standard assumptions for the evolution of this string network and the radiation
from it, axions must have a mass of $\ma\sim 100\mu{\rm eV}$ with large
specified uncertainties. We discuss critically the various suggestions in the
literature that the axion mass migh be lighter.
